Question

The length of a rectangle increases by 10% and the breath diminished by 25%. How does its area change?​

Answer 1

Answer:

★ Change in Area = 17.5 % ★

Explanation:

Given:

• Length of rectangle is increased by 10%
• Breadth of rectangle is decreased by 25%

To Find:

• Change in the area of Rectangle

Solution: Let the Length of rectangle be x and Breadth be y

A/q

★ Length is increased by 10% ★

$\small\implies{\sf }$ Length = x + 10 % of x

$\small\implies{\sf }$ Length = x + 10/100 (x) = 1.1x

★ Breadth is decreased by 25% ★

$\small\implies{\sf }$ Breadth = y – 25% of y

$\small\implies{\sf }$ Breadth = y – 25/100(y) = 0.75y

★ Area of rectangle =Length x Breadth★

$\small\implies{\sf }$ Area of rectangle = x(y)

$\small\implies{\sf }$ Area = (1.1x)(0.75y) = 0.825xy

Therefore, Change in Area =

$\small\implies{\sf }$ xy – 0.825xy = 0.175xy

∴ Percentage change in area = (Change in Area/ Original Area x 100 )

$\small\implies{\sf }$ Percentage Change = 0.175xy/xy (100)

$\small\implies{\sf }$ 0.175 x 100 = 17.5 %

Hence, Change in Area = 17.5 %

Answer 2

consider image for your answer

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