Question

The base of a rectangle is 40cmand perimeter is100cm. What is the area and height of the rectangle?

Short answer

The area of the rectangle is$400c{m}^2$ and height is10cm .

Step-by-step solution

Step 1. Given information.

Base of the rectangle$b=40cm$

Perimeter of the rectangle$P=100cm$ .

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 :

$\begin{array}{c}P=2(b+h)\\ 100=2(40+h)\\ 50=40+h\\ h=50-40\\ h=10cm\end{array}$

Area of the rectangle:

$\begin{array}{c}A=b\times h\\ =40\times 10\\ =400c{m}^2\end{array}$

Therefore, the area of the rectangle is$400c{m}^2$ and height is 10cm