Chapter 6, Problem 24SGR

To determine

To calculate:

The variables, system of equations and its solution set for the given condition using the substitution method

Answer to Problem 24SGR

In the given system, two variables are defined as length $\left(l\right)$ and width of a rectangle as $\left(w\right)$ respectively. The system of equations is $2l+2w=48$ and $l=6+w$ . The length and width of rectangle is $15inches$ and $9inches$ respectively.

Explanation of Solution

Given information:

Perimeter of a rectangle: $48in$

Length is $6in$ greater than the width.

Calculation:

Consider,

Length of a rectangle: $l$

Width of a rectangle: $w$

As per conditions of problem:

  $2l+2w=48$........(1)

  $l=6+w$........(2)

Put the value of $l$ in eq. (1):

  $\begin{array}{l}2l+2w=48\\ 2\left(6+w\right)+2w=48\\ 12+2w+2w=48\\ 12+4w=48\\ 4w=36\\ w=9\end{array}$

Calculate the value of $l$ by using the eq.(2):

  $\begin{array}{l}l=6+w\\ l=6+9\\ l=15\end{array}$

Hence the length and width of rectangle is calculated as:

  $\begin{array}{l}l=15inches\\ w=9inches\end{array}$