Q11. - Geometry

Question

The base of a rectangle is 16cm and perimeter is42cm . What is the area and height of the rectangle?

Step-by-Step Solution

Answer

The area of the rectangle is$80c{m}^2$ and height is5cm .

Step 1. Given information.

Base of the rectangle$b=16cm$

Perimeter of the rectangle$P=42cm$ .

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 & height of the rectangle.

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

Height of the rectangle :

$\begin{array}{c}P=2(b+h)\\ 42=2(16+h)\\ 21=16+h\\ h=21-16\\ h=5cm\end{array}$

Area of the rectangle:

$\begin{array}{c}A=b\times h\\ =16\times 5\\ =80c{m}^2\end{array}$

 

Therefore, the area of the rectangle is$80c{m}^2$ and height is 5cm