Question

Geometry Find the value of x for the given triangle, rectangle or square.

Perimeter = 32 units

Short answer

The value of x is 2.

Step-by-step solution

Step 1. Given

Perimeter = 32 units, length is x unit and width is $2x+10$.

Step 2.  To determine

We have to find the value of the x for the given rectangle.

Step 3. Calculation

The equation of the perimeter will be$2\left[x+\left(2x+10\right)\right]=40$

$\begin{array}{l}2\left[x+\left(2x+10\right)\right]=32\\ 2\left[x+2x+10\right]=32\left[\text{combineliketerms}\right]\\ 2\left(3x+10\right)=32\left[\text{distributiveproperty}\right]\\ 6x+20=32\\ 6x+20-20=32-20\left[\text{subtract20fromeachside}\right]\\ 6x=12\\ 6x÷6=12÷6\left[\text{divideeachsideby6}\right]\\ x=2\end{array}$

Hence, the required value of x is 2.