The sides of a triangle are in the ratio 4 : 5 : 7. If its perimeter is 48 inches, then what is the difference between its two bigger sides?

Question

Question

This question was previously asked in

Maha TAIT Official Paper (Held On 12 Dec 2017 Shift 1)

Answer 1

Concept Used:-

The perimeter of a triangle is the sum of each of its sides. Suppose a, b, and c are the sides of a triangle. Thus, its perimeter,

⇒ P = a + b + c

Explanation:-

Given that, the sides of a triangle are in the ratio 4 : 5 : 7. Suppose the sides of the triangle are 4x, 5x and 7x.

Here, perimeter of the triangle, P = 48 inches. Thus,

⇒ P = 4x + 5x + 7x

⇒ 48 = 16x

Divide both side by 16,

⇒ 48 / 16 = x

⇒ 3 = x

⇒ x = 3 inches

Now, the sides of triangles,

⇒ 4x = 4 × 3 = 12 inches

⇒ 5x = 5 × 3 = 15 inches

⇒ 7x = 7 × 3 = 21 inches

Here, 15 and 21 are the bigger sides of the triangle. So, the difference between these sides,

⇒ 21 - 15 = 6 inches

So, the difference between its two bigger sides is 6 inches.

Hence, the correct option is 2.