Chapter 6, Problem 24SGR

To determine

Tocalculate : a. To define and to write the system of equations to find the length and breadth of the rectangle.

Answer to Problem 24SGR

System of the equations to find the length and breadth of the rectangle are:

  $a+b=24$

  $a=b+6$

Length of the rectangle is 15 inches.

And breadth of the rectangle is 9 inches

Explanation of Solution

Given information :

Given:

The perimeter of the rectangle is 48 inches.

The length is 6 inches greater than width.

Formula used :

If a and b are the length and width of the rectangle respectively:

The perimeter of the rectangle $=2(a+b)=48$

For substitution method, we substitute the value of anyone first variable from first equation to other equation then we find the value of the first variable from that second equation, where there is only one variable unknown. After getting the value of the first variable, we put the value of this variable to any of the two linear equations. And then we find the value of the second variable.

Calculation :

Let:

The length of the rectangle is a.

And the breadth of the rectangle is b.

Perimeter of the rectangle $=2(a+b)=48$

  $\Rightarrow a+b=\frac{48}{2}$

  $\Rightarrow a+b=24$ ........Equation 1

Since the length is 6 inches greater than the width so

  $a=b+6$ ........ Equation 2

Putting the value of a from Equation 2 in Equation 1

  $\begin{array}{l}(b+6)+b=24\\ \Rightarrow 2b+6=24\\ \Rightarrow 2b=24-6\\ \Rightarrow 2b=18\\ \Rightarrow b=\frac{18}{2}\\ \Rightarrow b=9\end{array}$

Putting the value of b into Equation 2, we get:

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

So length of the rectangle is 15 inches.

And breadth of the rectangle is 9 inches.