The perimeters of five squares are 24 cm,32 | vedclass

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Question

(C) The side length of a square is given by $s = \frac{	ext{Perimeter}}{4}$.The sides of the five squares are:$s_1 = \frac{24}{4} = 6 \ cm$,$s_2 = \f

Vedclass · Accepted Answer

$124$

Vedclass · Answer

(C) The side length of a square is given by $s = \frac{	ext{Perimeter}}{4}$.The sides of the five squares are:$s_1 = \frac{24}{4} = 6 \ cm$,$s_2 = \frac{32}{4} = 8 \ cm$,$s_3 = \frac{40}{4} = 10 \ cm$,$s_4 = \frac{76}{4} = 19 \ cm$,$s_5 = \frac{80}{4} = 20 \ cm$.The sum of the areas of these squares is:$A = (6^2 + 8^2 + 10^2 + 19^2 + 20^2) \ cm^2$$A = (36 + 64 + 100 + 361 + 400) \ cm^2 = 961 \ cm^2$.Let the side of the new square be $S$. Since its area is equal to the sum of the areas of the five squares:$S^2 = 961 \ cm^2$$S = \sqrt{961} = 31 \ cm$.The perimeter of the new square is $P = 4 	imes S = 4 	imes 31 = 124 \ cm$.

The perimeters of five squares are $24 \ cm$,$32 \ cm$,$40 \ cm$,$76 \ cm$,and $80 \ cm$ respectively. The perimeter of another square equal in area to the sum of the areas of these squares is $...... \ cm$.

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