if the perimeter of a square increases of 25%,what is the increase in its area??...

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TithiShaw @TithiShaw

August 2021 1 11 Report

if the perimeter of a square increases of 25%,what is the increase in its area???

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ADITYA1100 Let the side of square be x.

Perimeter of square = 4x

Increase in perimeter = 25% of 4x

$= \frac{25}{100} \times 4x \\ \\ = \frac{100x}{100} \\ \\ = x$

New perimeter = 4x +x = 5x

Let the new side be y.

4y = 5x

$y = \frac{5}{4} x \\$
$old \: area = {x}^{2} \\ \\ new \: area \: = {y}^{2} \\ \\ = {( \frac{5}{4}x) }^{2} \\ \\ = \frac{25}{16} {x}^{2}$
Area increase = new area - old area

$= \frac{25}{16} {x}^{2} - {x}^{2} \\ \\ = {x}^{2} ( \frac{25}{16} - 1) \\ \\ = {x}^{2} ( \frac{25 - 16}{16} ) \\ \\ = {x}^{2} ( \frac{9}{4} ) \\ \\ = \frac{9}{4} times \: of \: old \: area$

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