Solve the applied problem.A rectangle is twice as long as it is wide. If it has an area of...

Solve the applied problem.

A rectangle is twice as long as it is wide. If it has an area of 24.5 square inches, what are its dimensions? [Hint: See Example 1.]

EXAMPLE 1

Set up the following problem: Arectangle is twice as long as it is wide. If it has an area of 24.5 square inches, what are its dimensions?

SOLUTION

Read: We are asked to find the length and width. Label: Let x denote the width and y the length, and draw a picture of the situation, as in Figure 1. Translate: Use the fact that the area of a rectangle is length × width.

Consolidate: Substitute y = 2x in the area equation:

So the equation to be solved is 2x2 = 24.5.

Figure 1