   Chapter 4.6, Problem 56PS

Chapter
Section
Textbook Problem

For Problems 45-56, set up an algebraic equation and solve each problem. (Objective 3)The perimeter of a rectangle is 114 centimeters. If the ratio of its width to its length is 7 to 12, find the dimensions of the rectangle.

To determine

To Find:

The dimensions of the rectangle.

Explanation

Approach:

The comparison of the two numbers by division, we can write in the form of the ratio a to b as ab. The statement of equality between two ratios is known as a proportion. Therefore if ab and pq are two same ratios, the proportion ratio can be formed ab=pq(b0,q0).

This property can be solved as follows.

ab=pq, (b0,q0)

Multiply bq on both sides.

bq(ab)=bq(pq)qa=bp

Calculation:

The perimeter of the rectangle can be expressed as.

perimeter=2(l+w)

Here, the length of the rectangle is l in cm and the width of the rectangle is w in cm

Substitute 114cm for perimeter in the above expression.

2(l+w)=114cml+w=114cm2

Further solving.

l+w=57cm (1)

For the given rectangle the ratio of width to length given as 512

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