Chapter 8.1, Problem 71PFA

To determine

To find the sum of the perimeters of one square and on equilateral triangle.

Answer to Problem 71PFA

  $14x+7$

Explanation of Solution

Given:

The sides of squares and triangle has the same length.

Length of the side: $2x+1$

Formula used:

Perimeter of Square: $4a$

Perimeter of Equilateral triangle: $3a$

where a is the side.

Calculation:

To find the perimeter of square, substitute the side in the formula for perimeter of square.

  $\begin{array}{c}4a=4(2x+1)\\ =8x+4\end{array}$

To find the perimeter of an equilateral triangle, substitute the side in the formula for perimeter of equilateral triangle.

  $\begin{array}{c}3a=3(2x+1)\\ =6x+3\end{array}$

The sum of the perimeters of square and perimeter is,

  $\begin{array}{l}\Rightarrow (8x+4)+(6x+3)\\ \Rightarrow 8x+6x+4+3\\ \Rightarrow 14x+7\end{array}$

Conclusion:

The sum of the perimeters of square and equilateral triangle is $14x+7.$