Q32. - Geometry

Question

The lengths of the sides of three squares are$s,(s+1),\&(s+2).$  If their total area is$365c{m}^2$ , find their total perimeter.

Step-by-Step Solution

Answer

The total perimeter.$P=132cm$

Step 1. Given information.

The length of the sides of three squares is$s,s+1,s+2$ .

Total area $A=365c{m}^2$

Step 2. Concept Used.

The area of the square is 
$A={\left(side\right)}^2$

Step 3. Let’s calculate the area of each square and the value of s.

According to the given sides of the squares are$s,s+1,s+2$

The side of first square=s

Area=$s^2$

The side of second square=$s+1$

Area=${(s+1)}^2$

The side of third square=$s+2$

Area=${(s+2)}^2$

Now,

Total area is;

$\begin{array}{c}365=s^2\text{Invalid <m:msup> element}\text{Invalid <m:msup> element}++\\ 365=s^2+s^2+1+2s+s^2+4+4s\\ 365=3s^2+6s+5\end{array}$

Solve this quadratic equation.

$\begin{array}{c}3s^2+6s-360=0\\ (s-10)(s+12)=0\\ s=10\end{array}$