Q13. - Geometry

Question

The base of a rectangle is $(a+3)$  and height $(a-3)$ . What is the area and perimeter of the rectangle?

Step-by-Step Solution

Answer

The area of the rectangle is $(a^2-9)c{m}^2$  and perimeter is $\left(4a\right)cm$ .

Step 1. Given information.

Base of the rectangle  $b=(a+3)$

Height of the rectangle  $h=(a-3)$ .

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 :

 $\begin{array}{c}A=(a+3)\times (a-3)\\ =(a^2-9)c{m}^2\end{array}$

Formula used- $(a^2-b^2)=(a+b)(a-b)$

Perimeter of the rectangle:

 $\begin{array}{c}P=2(a+3+a-3)\\ =2\left(2a\right)\\ =\left(4a\right)cm\end{array}$

Therefore, the area of the rectangle is$(a^2-9)c{m}^2$  and perimeter is  $\left(4a\right)cm$