Question

When each side of a particular square is lengthened by $2$ inches, the area of the square increases by $32$ square inches. Calculate the length of sides of original square(in inches).

• A. $4$
• B. $5$
• C. $6$
• D. $7$
• E. $8$

Answer 1

The correct option is D $7$

Let the original side be $x$ inches
So area $=x\times x$
If the sides are increased by $2$ inches
New area $=(x+2)(x+2)$
According to question:
New area $-$ area $=32$
So $(x+2)(x+2)-x\times x=32$
$\Rightarrow x\times x+4x+4-x\times x=32$
$\Rightarrow 4x+4=32$
$\Rightarrow 4x=28$
$\Rightarrow x=7$ inches