Question
Download Solution PDFThe station master decided to increase the length of a rectangular digital board by 3% and decrease its width by 3%. Find the total change in the area of the board.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The station master decided to increase the length of a rectangular digital board by 3% and decrease its width by 3%.
Concept:
The change in area can be determined by using the formula for percentage change in area when dimensions are changed by certain percentages.
Formula Used:
Percentage change in area = (Percentage change in length + Percentage change in width + Percentage change in length × Percentage change in width / 100)
Calculation:
We have,
⇒ Percentage change in length = +3%
⇒ Percentage change in width = -3%
⇒ Percentage change in area = 3 + (-3) + (3 × -3) / 100
⇒ Percentage change in area = 3 - 3 - 9 / 100
⇒ Percentage change in area = 0 - 0.09
⇒ Percentage change in area = -0.09%
∴ The total change in the area of the board is a 0.09% decrease.
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