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Chapter 7: Q. 7.161 (page 890)

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

Expert verified

The length of the rectangle is6ftand width is5ft.

Step by step solution

01

Step 1. Given Information.

The area of the rectangle is 30ft2.

Also,

The length is 1ftmore than the width.

02

Step 2. Factor the equation.

Let the width of the rectangle is xft.

Therefore, the length is (x+1)ft

Therefore,

x(x+1)=30x2+x=30x2+x-30=0x2+6x-5x-30=0x(x+6)-5(x+6)=0(x+6)(x-5)=0

03

Step 3. Solution of the equation.

Using the Zero product property,

x=5,x=-6Neglectingx=-6becauselengthcannotbenegative.Therefore,x=5x+1=6

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