Chapter 11: Q32. (page 427)

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

Short Answer

Expert verified

The total perimeter. $P = 132 c m$

Step by step solution

Step 1. Given information.

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

Total area $A = 365 c m^{2}$

Step 2. Concept Used.

The area of the square is
$A = {(s i d e)}^{2}$

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;

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

Solve this quadratic equation.

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

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

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The lengths of the sides of three squares ares,(s+1),&(s+2).If their total area is365cm2, find their total perimeter.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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