Q16. - Geometry

Question

The area of a rectangle is$(y^2+7y)$  and height $\left(y\right)$. What is the perimeter and base of the rectangle?

Step-by-Step Solution

Answer

The perimeter of the rectangle is$(4y+14)$ and base is$(y+7)$ .

Step 1. Given information.

Area of the rectangle$A=(y^2+7y)$

Height of the rectangle$h=\left(y\right)$ .

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 base & perimeter of the rectangle.

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

 of the rectangle :

$\begin{array}{c}A=\left(b\right)\times \left(h\right)\\ y^2+7y=\left(b\right)\times y\\ b=\frac{y^2+7y}{y}\\ b=y+7\end{array}$

Perimeter of the rectangle:

$\begin{array}{c}P=2(y+7+y)\\ =2(2y+7)\\ =(4y+14)\end{array}$

Therefore, the perimeter of the rectangle is$(4y+14)$ and base is$(y+7)$