Chapter 8.8, Problem 59STP

To determine

The value of x

Answer to Problem 59STP

The value of x is $x=8$

Option C is correct

Explanation of Solution

Given:

The perimeters of the two sections are equal and w represents the width of the rectangle

  

Concept Used:

Perimeter of rectangle $P=2\left(length+width\right)$

Perimeter of Triangle $P=Side+Side+Side$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the perimeters of the rectangle $P=2\left(length+width\right)$ as below:

  $\begin{array}{c}P=2\left(length+width\right)\\ length=x+4\\ width=x-2\\ P=2\left(x+4+x-2\right)\\ =2\left(2x+2\right)\\ =2\cdot 2x+2\cdot 2\\ p=4x+4\end{array}$

In order to find the perimeters of the triangle $P=Side+Side+Side$ as below:

  $\begin{array}{c}P=Side+Side+Side\\ P=\left(x+3\right)+\left(x+4\right)+\left(x+5\right)\\ P=3x+12\end{array}$

Both are equal, thus the equation is $4x+4=3x+12$

In order to solve the equation $4x+4=3x+12$ first subtract both sides by $3x$ and then subtract both sides by $4$ and then simplify further as below:

  $\begin{array}{c}4x+4=3x+12\\ 4x+4-3x=3x+12-3x\\ x+4=12\\ x+4-4=12-4\\ x=8\end{array}$

Thus, the value of x is $x=8$

Option C is correct