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 a side of the original square.

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

Answer 1

The correct option is D $7$

Let each side of a square be $x$
When each side is increased by $2$ inches side will be $(x+2)$
It is said that area will also increase by $32$ square inches.
So as per given, sum equation will be
${(x+2)}^2=x^2+32$
$\Rightarrow x^2+2x.2+2^2=x^2+32$
$\Rightarrow 4x+4-32=0$
$\Rightarrow 4x=28$
$\Rightarrow x=7$
Length of a side of the original square will be $7$ inches.