Q12. - Geometry

Question

The base of a rectangle is $(x+5)$ and height$\left(x\right)$ . What is the area and perimeter of the rectangle?

Step-by-Step Solution

Answer

The area of the rectangle is$(x^2+5x)$ and perimeter is$(4x+10)$ .

Step 1. Given information.

Base of the rectangle$b=(x+5)$

Height of the rectangle$h=\left(x\right)$ .

Step 2. Concept Used.

If b is the base of the reactangle and h is the height of the rectangle.

Then, the   area of the rectangle is $A=b\times h$

Perimeter of the rectangle is

$P=2(b+h)$

Step 3. Let’s calculate the area & perimeter of the rectangle.

Put the value of base and height  into the formula and find the area.

Area of the rectangle :

$\begin{array}{c}A=(x+5)\times \left(x\right)\\ =(x^2+5x)c{m}^2\end{array}$

Perimeter of the rectangle:

$\begin{array}{c}P=2(x+5+x)\\ =2(2x+5)\\ =(4x+10)cm\end{array}$

Therefore, the area of the rectangle is$(x^2+5x)c{m}^2$ and perimeter is $(4x+10)cm$