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Pre-algebra

Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

$Math Studyset Vaia Explanations$ Math

Common Core Edition · 183 pages

ISBN: 9780547587776

Chapter 3: Q29. (page 133)

Find the perimeter of the square.

Short Answer

Expert verified

The required perimeter of the square is 288

Step by step solution

01

Step-1 – Given

Two sides of the square are $12 x$ and $7 x + 30$ .

02

Step-2 – To determine

We have to find the perimeter of the square.

03

Step-3 – Calculation

We know that each sides of a square are equal.

So, $12 x = 7 x + 30$

Then we solve the equation:

\begin{array}{l} 12 x = 7 x + 30 writetheequation \\ 12 x - 7 x = 30 + 7 x - 7 x subtract7xfrombothsides \\ 5 x = 30 simplify \\ \frac{5 x}{5} = \frac{30}{5} divideeachsideby5 \\ x = 6 simplify \end{array}

Substituting the value of x in the expression of a side = $12 x$ we get:

$\begin{array}{l} 12 x \\ = 12 \times 6 Substitutethevalueof x \\ =72Multiply \end{array}$

So the length of each side = 72

Hence,

$\begin{array}{l} Perimeter (P) = 4 \times eachsideofthesqaure \\ Perimeter (P) = 4 \times 72 Substitutethevalueintheformula \\ Perimeter (P) = 288 unitsMultiply \end{array}$

Therefore, $Perimeter (P) = 288$

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