Question

Find the perimeter of the square.

Short answer

The required perimeter of the square is 288

Step-by-step solution

Step-1 – Given

Two sides of the square are $12x$ and $7x+30$.

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, $12x=7x+30$

Then we solve the equation:

$\begin{array}{l}12x=7x+30\text{writetheequation}\\ 12x-7x=30+7x-7x\text{subtract7xfrombothsides}\\ 5x=30\text{simplify}\\ \frac{5x}{5}=\frac{30}{5}\text{divideeachsideby5}\\ \text{x}=6\text{simplify}\end{array}$

Substituting the value of x in the expression of a side = $12x$we get:

$\begin{array}{l}12x\\ =12\times 6\text{Substitutethevalueof}x\\ \text{=72Multiply}\end{array}$

So the length of each side = 72

Hence,

$\begin{array}{l}\text{Perimeter}\left(P\right)=4\times \text{eachsideofthesqaure}\\ \text{Perimeter}\left(P\right)=\text{4}\times 72\text{Substitutethevalueintheformula}\\ \text{Perimeter}\left(P\right)=288\text{unitsMultiply}\end{array}$

Therefore, $\text{Perimeter}\left(P\right)=288$