Chapter 1.7, Problem 14P

To determine

To calculate: Solve using the five step plan. Write out each step. A choice of possible numbers for one unknown is given.The length of a rectangle is $3\frac{1}{2}$ times its width. Its perimeter is 108 cm. Find its length and width. Choices for the width: 12, 14, 24.

Answer to Problem 14P

The width of rectangle is $a=12m$ and the length of rectangle is $3.5\left(12\right)=42m$

Explanation of Solution

Given information:The length of a rectangle is $3\frac{1}{2}$ times its width. Its perimeter is 108 cm.

Calculation:

Step 1: Here we have two unknowns, length and width of rectangle.

Step 2: Let $a$ be the width of rectangle and $3.5a$ be the length of rectangle.

Step 3: As given, the perimeter of the car is 108, such that $2a+2\left(3.5a\right)=108$

Step 4: Choices for $a$ are given as 12, 18, 24.

$a$	$2a+2\left(3.5a\right)=108$	True / False
12	$2\left(12\right)+2\left(3.5*12\right)=108$	True
18	$2\left(18\right)+2\left(3.5*18\right)=108$	False
24	$2\left(24\right)+2\left(3.5*24\right)=108$	False

From above table we can say that the width of rectangle is $a=12m$ and the length of rectangle is $3.5\left(12\right)=42m$

Step 5: Now we verify the answer

The length is 3.5 times of width: $108m$ , which is correct

The perimeter is $108m$ : $2\left(12\right)+2\left(42\right)=108$ , which is also correct.