Rectangle MCQ Quiz - Objective Question with Answer for Rectangle - Download Free PDF

Given:

Length of the floor (L) = 7.5 m

Breadth of the floor (B) = 2 m

Number of tiles = 40

Area of each tile = (1/16) m²

Formula used:

Total area of the floor = L × B

Total area covered by tiles = Number of tiles × Area of each tile

Non-tiled area = Total area of the floor - Total area covered by tiles

Ratio of tiled to non-tiled area = Area covered by tiles : Non-tiled area

Calculations:

Total area of the floor = 7.5 × 2

⇒ Total area of the floor = 15 m²

Total area covered by tiles = 40 × (1/16)

⇒ Total area covered by tiles = 40 × 0.0625

⇒ Total area covered by tiles = 2.5 m²

Non-tiled area = Total area of the floor - Total area covered by tiles

⇒ Non-tiled area = 15 - 2.5

⇒ Non-tiled area = 12.5 m²

Ratio of tiled to non-tiled area = 2.5 : 12.5

⇒ Ratio = 1 : 5

∴ The correct answer is option (4).

Given:

Length (L) = 2 × Breadth (B)

Area (A) = 128 sq. feet

Formula used:

Area of Rectangle = Length × Breadth

Calculation:

128 = (2 × B) × B

⇒ 128 = 2B²

⇒ B² = 64

⇒ B = √64

⇒ B = 8 feet

∴ The correct answer is option (1).

Given:

Reduction in length = 11%.

Reduction in breadth = 11%.

Formula Used:

% Decrease in Area = (Reduction in Length + Reduction in Breadth - (Reduction in Length × Reduction in Breadth))%

Calculation:

Reduction in Length = 11% = 11/100 = 0.11

Reduction in Breadth = 11% = 11/100 = 0.11

% Decrease in Area = (0.11 + 0.11 - (0.11 × 0.11)) × 100

⇒ % Decrease in Area = (0.11 + 0.11 - 0.0121) × 100

⇒ % Decrease in Area = (0.2079) × 100

⇒ % Decrease in Area = 20.79%

The % decrease in the area is 20.79%.

Given:

In measuring the sides of a rectangle, one side is taken 10% in excess, and the other 8% in deficit.

Formula used:

Error Percent in Area = (Percentage Error in Length + Percentage Error in Width + Percentage Error in Length × Percentage Error in Width)

Calculation:

Let the original length be L and the original width be W.

Measured Length = L + 0.10L = 1.10L

Measured Width = W - 0.08W = 0.92W

Error in Length = 10%

Error in Width = -8%

Percentage Error in Area = 10% + (-8%) + (10% × -8% / 100)

⇒ Percentage Error in Area = 10 - 8 + (10 × -8 / 100)

⇒ Percentage Error in Area = 2 - 0.8

⇒ Percentage Error in Area = 1.2%

∴ The correct answer is option (3).

Given:

The ratio of length to breadth = 4 : 5

The length is 20 meters less than the breadth.

Formula used:

Perimeter of a rectangle = 2 × (Length + Breadth)

Calculation:

Let the length = 4x and the breadth = 5x

Length = Breadth - 20

4x = 5x - 20

⇒ 4x - 5x = -20

⇒ -x = -20

⇒ x = 20

The length = 4x = 4 × 20 = 80 meters

The breadth = 5x = 5 × 20 = 100 meters

The perimeter of a rectangle = 2 × (Length + Breadth)

Perimeter = 2 × (80 + 100) = 2 × 180 = 360 meters

∴ The perimeter of the vacant space is 360 meters.

Formula used

Area = length × breath

Calculation

The garden EFGH is shown in the figure. Where EF = 220 meters & EH = 70 meters.

The width of the path is 4 meters.

Now the area of the path leaving the four colored corners

= [2 × (220 × 4)] + [2 × (70 × 4)]

= (1760 + 560) square meter

= 2320 square meters

Now, the area of 4 square colored corners:

4 × (4 × 4)

{∵ Side of each square = 4 meter}

= 64 square meter

The total area of the path = the area of the path leaving the four colored corners + square colored corners

⇒ Total area of the path = 2320 + 64 = 2384 square meter

∴ Option 4 is the correct answer.

Given:

Length of outer rectangle = 112 m

Breadth of the outer rectangle = 78 m

Breadth of road = 2.5 m

Formula used:

Area of road = Area of the plot − Area without road

Area of rectangle = Length × breadth

Calculation:

From the figure:

Length of inner rectangle = (78 - 5) = 73 m

Breadth of inner rectangle = (112 - 5) = 107 m

Area of road = Area of the rectangular plot − Area of inner rectangle

⇒ A  =  (112 × 78) − (107 × 73) 

⇒ A  = 8736 − 7811

⇒ A  = 925 m²

The area of the path is 925 m²

Alternate Method

Concept used:

If length of a rectangle = L, breadth = B and width of  path = W

If the path is inside the rectangle, then

Area of the path = (L + B - 2W) × 2W

Calculation:

According to the question,

L = 112, B = 78 and W = 2.5

The area of the path = (112 + 78 - 5) × 5 =  925 m2

Given:

Two rectangles are of the same area equal = 480 cm²

They differ in length by 6 cm and breadth by 4 cm

Formula used:

Area of rectangle = l × b

Perimeter of rectangle = 2(l + b)

Where, l = length and b = breadth

Shortcut Trick

For the same figure,

The difference in perimeter = Difference in the sum of sides

⇒ P₁ - P₂ = 2(l + b) - 2(l + 6 + b - 4)

⇒ P1 - P2 = 2(6 - 4) = 4

Alternate Method

Let the length and breadth of two rectangles be l₁b₁ and l₂b₂ respectively.

According to the question

⇒ l₁b₁ = 480         ------(1)

⇒ l₂b₂ = 480         ------(2)

They differ in length by 6 cm and breadth by 4 cm

Then, length of second rectangle (l₂) = (l₁ + 6) cm

Then, breadth of second rectangle (b₂) = (b₁ – 4) cm

Perimeter of first rectangle = 2(l₁ + b₁) 

Perimeter of second rectangle = 2(l₁ + 6 + b₁ – 4)

⇒ 2(l₁ + b₁) + 4 

The difference in their perimeters is

⇒ 2(l1 + b1) – 2(l1 + b1) + 4

⇒ 4 cm

∴ The required difference in their perimeters is 4 cm.

Mistake PointsIf the length of the first rectangle increases then to make the area

the same, the breadth will decrease.

Given:

Length : breadth = 3 : 2

Length is increased by 5 m keeping the breadth same

New area become 2600 m2

Formula used:

Area of rectangle = Length × breadth 

Perimeter = 2 (Length + breadth)

Calculation:

Let length & breadth be '3y' & '2y' respectively.

According to the question

⇒ (3y + 5) × 2y = 2600

⇒ 6y² + 10y = 2600 

⇒ 6y² + 10y - 2600 = 0

⇒ 3y² + 5y - 1300 = 0

⇒ 3y² - 60y + 65y - 1300 = 0

⇒ 3y(y - 20) + 65(y - 20) = 0

⇒ (3y + 65)(y - 20) = 0

⇒  y = 20, y ≠ - (65/3)

Since, length can not be negative.

Therefore, length & breadth of original rectangle

3y = 3 × 20 = 60

2y = 2 × 20 = 40

Hence, perimeter = 2(60 + 40) = 200

∴ Perimeter of the rectangle is 200 m.

Given:

The length and breadth of a rectangle are increased by 8% and 5%, respectively. 

Concept used:

Final percentage change after two successive increments of A% and B% = \((A + B + {AB \over 100})\%\)

Calculation:

Final percentage increment in area = \(8 + 5 + \frac {8 \times 5}{100}\) = 13.4%

∴ The area will increase by 13.4%.

Area of a rectangle = Length × breadth

⇒ 168 = Length × 7

⇒ Length = 168/7

⇒ Length = 24 cm

We know that,

Diagonal² = Length² + breadth²

⇒ Diagonal² = 24² + 7² = 576 + 49 = 625

Given:

length and breadth of a room is 15 m 17 cm and 9 m 2 cm respectively

Formula used:

Area of the square = Side²

Number of square tiles = (Area of the room)/Area of square tiles

Concept used:

1 m = 100 cm

Calculation:

Length = 15 m 17 cm = (15 × 100 + 17) cm = 1517 cm

Breadth = 9 m 2 cm = (9 × 100 + 2) cm = 902 cm

So, the size of the square tiles will be the HCF of 1517 and 902

⇒ 1517 = 37 × 41 and 902 = 2 × 11 × 41

So, size of square tiles = 41 cm 

Area of square tiles = (41 × 41) sq. cm

Also area of the room = (1517 × 902) sq. cm

Number of square tiles = (Area of the room)/Area of square tiles

⇒ number of square tiles = (1517 × 902)/(41 × 41) = 814

∴ The Minimum number of square tiles is 814

Given:

Dimensions of rectangular sheet = 28 cm × 16 cm

Length of the square = 3 cm

Formula:

The volume of Box = l × b × h

where, l, b, h = Length, breadth, and height of the box respectively  

Calculation:

l = 28 − 2(3)

⇒ 28 - 6 = 22 cm

b = 16 - 2(3) = 16 - 6

⇒ b = 10 cm

h = 3 cm

Volume of box = 22 × 10 × 3

 ∴ The volume of the box is 660 cm³.

Given:

A field is in the shape of a rectangle of length 90 m and breadth 75 m.

In one corner of the field, a pit, which is 18 m long 15 m broad, and 6 m deep, has been dug out

Concept used:

Volume = L × B × H

Surface area = L × B

Calculation:

According to the question,

The total area of the field = 90 × 75 = 6750 m² 

Area of the pit = 18 × 15 = 270 m² 

Remaining area = 6750 - 270 = 6480 m2 

The volume of the pit = 18 × 15 × 6 = 1620 m³ 

While spreading the dug-out earth on the remaining field,

The volume of the pit = Volume of the remaining field

⇒ 1620 = 6480 × H

⇒ H = \(\frac{1620}{6480}\) = \(\frac{1}{4}\) m or 25 cm

∴ The rise in the level of the field is 25 cm.

Given : 

Length of rectangle is twice it's breadth.

Length decreases by 4 cm and breadth increases by 4 cm.

Area of rectangle increases by 52 cm².

Formula used : 

Area of rectangle = Length × Breadth

Calculation : 

According to question,

⇒ L = 2B

⇒ L/B = 2x/1x

Area of rectangle = 2x²

Now,

⇒ (2x - 4) × (x + 4) = 2x² + 52

⇒ 2x² + 8x - 4x -16 = 2x2 + 52

⇒ 4x = 68

⇒ x = 17

Length of rectangle = 2x = 2 × 17 = 34 cm

∴ The correct answer is 34 cm.