Question

A square yard has area $1764$ m${}^2$. From a corner of this yard, another square part of area $784$ m${}^2$ is taken out for public utility. The remaining portion is divided in to $5$ equal square parts. What is the perimeter of each of these equal parts?

Answer 1

Let $a$ be the length of each side of a square yard.

A square yard has area $1764m^2$

$⟹$ Area of yard $=a^2$

$⟹{1764}^2=a^2⟹a=42$

$\therefore$ Length of each side$\left(a\right)=42m$

The square $B$ with dotted lines shows the area taken out for public utility

Let $b$ be the length of side of a square part $B$ which is taken out.

$\therefore$ Area of the square part taken out $=b^2$

$⟹784=b^2$

$⟹b=28m$

$\therefore$ Length of each side a square $B$ is $28m$

$A$ denotes the remaining part after B is taken out.

Now, the length of two sides of $A$ is $42-28=14m$ and other two sides are of length $42$.

Area of $A=$ Total area $-$ Area of $B$

$=1764-784=980m^2$

To divide $A$ into $5$ equal squares, we divide the area by $5$

$\frac{\text{Area of A}}{5}=\frac{980}{5}=196m^2$

$\therefore$ Area of each smaller squares will be $196m^2$

Let $c$ be the length of side of each square.

$⟹$ Area of each square $=c^2$

$⟹196m^2=c^2⟹c=14m$

$\therefore$ Length of each side is $14m$

Thus, the perimeter of each smaller squares $=4\times 14=56m$

Hence, the answer is $56m$