Q26. - Geometry

Question

The length of a rectangle is 12cm more than its width. Find the area of the rectangle if its perimeter is 100cm. 

Step-by-Step Solution

Answer

The area of the rectangle is  $589c{m}^2.$

Step 1. Given information.

Length of the rectangle $\left(h\right)12cm$ more than its width.

Perimeter of the rectangle $P=100cm$.

Step 2. Concept Used.

If bis the base of the reactangle and h is the length 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.

Let$\left(x\right)$ be the width, 

Then,

The length of the rectangle is 12cm more than its width.

i.e.

$length\left(h\right)=x+12$

 

Put the value of length and perimeter into the formula and find the value of x .

 

Perimeter of the rectangle:

$\begin{array}{c}P=2(b+h)\\ 100=2(x+x+12)\\ 100=2(2x+12)\\ 50=2x+12\\ 2x=50-12\\ x=\frac{38}{2}\\ x=19\end{array}$

Now, put the value of x into the formula and find  area of the rectangle-

$\begin{array}{c}A=bh\\ =\left(x\right)(x+12)\\ =\left(19\right)(19+12)\\ =\left(19\right)\left(31\right)\\ =589c{m}^2\end{array}$

 

Therefore, the area of the rectangle is $589c{m}^2.$