Q11. - Algebra 1

Question

Find the value of x so that the figures have the same perimeter.

Step-by-Step Solution

Answer

The value of the $x=7$.

Step 1. Given information.

We have a diagram 

To find the value of the x if the perimeter of the both diagrams are same.

Step 2. Apply Formula.

Given both diagrams are rectangles

And, the perimeter of the rectangle is the sum of the sides of the rectangle.

So, the perimeter of the left rectangle of the given diagram is:

$2\left(x+x+3\right)$

The perimeter of the other rectangle of the given diagram is:

$2\left(14+x-4\right)$

Step 3. Calculation.

According to given condition:

$\begin{array}{l}2\left(x+x+3\right)=2\left(14+x-4\right)\\ \Rightarrow 2x+2x+6=28+2x-8\\ \Rightarrow 4x-2x=28-8-6\\ \Rightarrow 2x=28-14\\ \Rightarrow 2x=14\\ \Rightarrow x=7\end{array}$

Hence, the value of the $x=7$.