Chapter 7: Q. 7.161 (page 890)

A rectangular sign has an area of $30$ square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.

Short Answer

Expert verified

The length of the rectangle is $6 f t$ and width is $5 f t .$

Step by step solution

Step 1. Given Information.

The area of the rectangle is $30 f t^{2} .$

Also,

The length is $1 f t$ more than the width.

Step 2. Factor the equation.

Let the width of the rectangle is $x f t .$

Therefore, the length is $(x + 1) f t$

Therefore,

$x (x + 1) = 30 x^{2} + x = 30 x^{2} + x - 30 = 0 x^{2} + 6 x - 5 x - 30 = 0 x (x + 6) - 5 (x + 6) = 0 (x + 6) (x - 5) = 0$

Step 3. Solution of the equation.

Using the Zero product property,

$x = 5, x = - 6 N e g l e c t i n g x = - 6 b e c a u s e l e n g t h c a n n o t b e n e g a t i v e . T h e r e f o r e, x = 5 x + 1 = 6$

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A rectangular sign has an area of $30$ square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factor the equation.

Step 3. Solution of the equation.

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A rectangular sign has an area of 30square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factor the equation.

Step 3. Solution of the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Calculus

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

A rectangular sign has an area of $30$ square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.