Q15. - Geometry

Question

The base of a rectangle is $\left(x\right)$ and area $(x^2-3x)$. What is the area and perimeter of the rectangle?

Step-by-Step Solution

Answer

The perimeter of the rectangle is$(4x-6)$ and height is$(x-3)$ .

Step 1. Given information.

Base of the rectangle$b=\left(x\right)$

Area of the rectangle $A=(x^2-3x)$.

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

 $\begin{array}{l}A=b\times h\\ \end{array}$

Perimeter of the rectangle is

$P=2(b+h)$

Step 3. Let’s calculate the height & perimeter of the rectangle.

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

Area of the rectangle :

$\begin{array}{l}A=b\times h\\ (x^2-3x)=\left(x\right)\times \left(h\right)\\ h=\frac{(x^2-3x)}{x}\\ h=(x-3)\end{array}$

Perimeter of the rectangle:

$\begin{array}{c}P=2(x+x-3)\\ =2(2x-3)\\ =(4x-3)\end{array}$

Therefore, the perimeter of the rectangle is$(4x-6)$ and height  is $(x-3).$