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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 237 (page 1148)

Jules purchased a microwave for his kitchen. The diagonal of the front of the microwave measures 26 inches. The front also has an area of 240 square inches. What are the length and width of the microwave?

Short Answer

Expert verified

$(24, 10), (10, 24)$

Step by step solution

01

Step 1. Given information.

The value of the diagonal of the front of the microwave is 26 inches and the front area of the microwave is 240 square inches.

02

Step 2. Forming the equations.

Let $l$ and $w$ represent the length and the width of the front of the microwave in inches. According to the given conditions, the diagonal role="math" localid="1645978557350" $\sqrt{l^{2} + w^{2}} = 26 l^{2} + w^{2} = 676 - - - > (1)$

The front area

$l w = 240 - - - > (2)$

03

Step 3. Solving the equations.

Solving equation (2) for l gives

$l = \frac{240}{w}$

Substituting this in (1) and simplifying:

${(\frac{240}{w})}^{2} + w^{2} = 676 \frac{57600}{w^{2}} + w^{2} = 676 w^{4} - 676 w^{2} + 57600 = 0 w^{4} - 100 w^{2} - 576 w^{2} + 57600 = 0 (w^{2} - 100) (w^{2} - 576) = 0 (w - 10) (w + 10) (w - 24) (w + 24) = 0$

Since width cannot be negative, either $(w - 10) = 0$ or $(w - 24) = 0$

When $(w - 10) = 0$ , then $w = 10$ and from (2), $l = \frac{240}{10} = 24$

When $(w - 24) = 0$ , then $w = 24$ and then $l = \frac{240}{24} = 10$

Expressing solution as ordered pairs: $(24, 10), (10, 24)$

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