Answered: The length of a rectangular garden is…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.13: Using Factoring To Solve Problems

Problem 9ST

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The length of a rectangular garden is 15 feet longer than its width. If the area of the garden is 286 square feet, what are the dimensions of the garden?

Length= _____feet

Width=______feet

Expert Solution

Step 1

The length of the garden is 15 feet longer than its width and the area of the garden is 286 square feet.

Let $x$ be the width of the garden.

Then, length of the garden is $x + 15$ .

Now, area of the rectangular garden is obtained by multiplying the length and width.

Therefore,

$\begin{array}{rcl} Area & = & length \times width \\ 286 & = & (x + 15) \cdot x \\ 286 & = & x^{2} + 15 x \end{array}$

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