The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq. cm. Find… · ABC26GN4429
Subject: General Aptitude · Chapter: Area
The difference of the areas of two 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 2 cm.
(a)7 cm
(b)9 cm
(c)11 cm
(d)16 cm
Answer
Answer (as printed): B
Explanation
Let the lengths of the line segments be $x \mathrm{cm}$ and $(x+2)$ cm . Then, $(x+2)^{2}-x^{2}=32 \Leftrightarrow x^{2}+4 x+4-x^{2}=32$ $$\begin{aligned} & \Leftrightarrow 4 x=28 \\ & \Leftrightarrow x=7 \end{aligned}$$ ∴ Length of longer line segment $=(7+2) \mathrm{cm}=9 \mathrm{cm}$.