Chapter 9.7, Problem 27STP

To determine

To choose : the correct answer.

Answer to Problem 27STP

Option D.is the correct answer.

Explanation of Solution

Given information :

The length x of a rectangle is $8$ inches more than the width y.

The perimeter is $49$ inches.

The given options:

A. $x+y=8$ and $4x+4y=49$

B. $x-8=y$ and $2x+2y=49$

C. $x=y-8$ and $x+y=49$

D. $x-y=8$ and $x+y=49$ .

Formula used:

The perimeter of a rectangle is given by:

  $P=2l+2w$

Calculation :

As per problem,

The length x of a rectangle is $8$ inches more than the width y.

The equation for length-width relationcan be written as:

  $x-8=y$

The perimeter of the rectangle of length x and width yis $49$ inches.

Substitute the value $49$ for P and x for length and y for width in the perimeter formula:

  $\begin{array}{l}P=2l+2w[\text{Write the formula]}\\ 49=2x+2y\text{ [Substitute }P=49,l=x,w=y]\end{array}$

Thus, the system of solution representing the given situation is:

  $\begin{array}{l}x-8=y\\ 2x+2y=49\end{array}$