Question

Find the perimeter of the square.

Short answer

The required perimeter of the square is 64

Step-by-step solution

Step-1 – Given

Two sides of the square are $4x$ and $36-5x$.

Step-2 – To determine

We have to find the perimeter of the square.

Step-3 – Calculation

We know that each sides of a square are equal.

So, $4x=36-5x\text{[Twosidesofthegivensqaure]}]$

Then we solve the equation:

$\begin{array}{l}4x=36-5x\text{writetheequation}\\ 4x+5x=36\text{add5xtobothsides}\\ 9x=36\text{simplify}\\ \frac{9x}{9}=\frac{36}{9}\text{divideeachsideby9}\\ x=4\end{array}$

Substituting the value of x in the expression of a side = $4x$we get:

$\begin{array}{l}4x\\ =4\times 4\text{Substitutethevalueof}x\\ \text{=16Multiply}\end{array}$

So the length of each side = 16

Hence,

$\begin{array}{l}\text{Perimeter}\left(P\right)=4\times \text{lengthofeachside}\\ \text{Perimeter}\left(P\right)=\text{4}\times \text{16Substitutethevalueintheformula}\\ \text{Perimeter}\left(P\right)=64\text{Multiply}\end{array}$

Therefore, $\text{Perimeter}\left(P\right)=64$