Q14. - Geometry

Question

The base of a rectangle is $(k+7)$ and perimeter $(4k+20)$. What is the area and height of the rectangle?

Step-by-Step Solution

Answer

The area of the rectangle is$(k^2+10k+21)$ and height  is$(k+3)$ .

Step 1. Given information.

Base of the rectangle$b=(k+7)$

Perimeter of the rectangle$P=(4k+20)$ .

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 base and perimeter  into the formula and find the height.

Height of the rectangle:

$\begin{array}{c}P=2(b+h)\\ 4k+20=2(k+7+h)\\ 4k+20=2k+14+2h\\ 2h=4k+20-14-2k\\ 2h=2k+6\\ h=\frac{2(k+3)}{2}\\ h=(k+3)\end{array}$

Area of the rectangle :

$\begin{array}{c}A=b\times h\\ =(k+7)\times (k+3)\\ =(k^2+7k+3k+21)\\ =(k^2+10k+21)\end{array}$

 Therefore, the area of the rectangle is$(k^2+10k+21)$ and heigh is $(k+3)$ .