Chapter 6.4, Problem 35PFA

To determine

To find the values of x and v

Answer to Problem 35PFA

$x=6$ inches and $v=42$ inches

Explanation of Solution

Given:

Perimeter of first rectangle: 120 inches

Perimeter of second rectangle: 180 inches

Concept used:

Forming linear equations from the given word problem and solving the system of linear equations with elimination method.

Perimeter of the rectangles = 2(length + breadth)

Calculation:

Consider the first rectangle,

Length of the rectangle = $2x+v$

Breadth of the rectangle = $x$

Perimeter = 2 ( x + ( $2x+v$ ))

  $\begin{array}{l}\Rightarrow 2(x+(2x+v))=120\\ \Rightarrow 2x+4x+2v=120\\ \Rightarrow 6x+2v=\mathrm{120....................................}(1)\end{array}$

Consider the second rectangle,

Length of the rectangle = $x+v$

Breadth of the rectangle = $v$

Perimeter = 2 ( x +( $2x+v$ ))

  $\begin{array}{l}\Rightarrow 2(v+(x+v))=180\\ \Rightarrow 2v+2x+2v=180\\ \Rightarrow 2x+4v=\mathrm{180....................................}(2)\end{array}$

Multiply equation (1) with 2,

  $\Rightarrow 12x+4v=\mathrm{240..................................}(3)$

Subtract equation (2) from equation (3),

  $\begin{array}{l}\Rightarrow (12x+4v)-(2x+4v)=240-180\\ \Rightarrow 10x=60\\ \Rightarrow x=6\end{array}$

Substitute the value of x in equation (2),

  $\begin{array}{l}\Rightarrow 2(6)+4v=180\\ \Rightarrow 12+4v=180\\ \Rightarrow 4v=180-12\\ \Rightarrow 4v=168\\ \Rightarrow v=42\end{array}$

Conclusion:

Therefore, the values are $x=6$ and $v=42$ .