The difference of the areas of two squares dr | vedclass

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Question

(B) Let the length of the greater line segment be $x \, cm$.Then,the length of the smaller line segment is $(x - 2) \, cm$.The area of the square form

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) Let the length of the greater line segment be $x \, cm$.Then,the length of the smaller line segment is $(x - 2) \, cm$.The area of the square formed by the greater line segment is $x^2 \, cm^2$.The area of the square formed by the smaller line segment is $(x - 2)^2 \, cm^2$.According to the problem,the difference between the areas is $32 \, cm^2$:$x^2 - (x - 2)^2 = 32$Using the identity $a^2 - b^2 = (a - b)(a + b)$:$(x - (x - 2))(x + (x - 2)) = 32$$(2)(2x - 2) = 32$Dividing both sides by $2$:$2x - 2 = 16$$2x = 18$$x = 9$Therefore,the length of the greater line segment is $9 \, cm$.

The difference of the areas of two squares drawn on two line segments of different lengths is $32 \, cm^2$. Find the length of the greater line segment if one is longer than the other by $2 \, cm$. (in $cm$)

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