Question

The difference of the areas oftwo squares drawn on two line segments of different lengths is $32$ sq. cm. Find the length of the greater line segment if one is longer than the other by $2cm.$

• A. $7cm$
• B. $9cm$
• C. $11cm$
• D. $16cm$

Answer 1

Answer: (B)

$9cm$

Let the length of the smaller line segment $=xcm$
Then, length of greater line segment $=(x+2)cm$
Given, $(x+2{)}^2-x^2=32$
$\Rightarrow x^2+4x+4-x^2=32$
$\Rightarrow 4x=32-4$
$\Rightarrow x=\frac{28}{4}=7cm$.
$\therefore$ Length of the greater line segment $=9cm.$