A rectangle lawn measures 60ft by 80ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new lawn is 2400 ft 2. How

Question

A rectangle lawn measures 60ft by 80ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new lawn is 2400 ft ². How wide is the sidewalk?

Answer 1

Draw a diagram:

We have a rectangle inside a rectangle.

 

The larger outside rectangle is the original lawn:  80ft by 60 ft with area 4800 ft²

 

The smaller inside rectangle is (80-2x)by(60-2x) where x is width of the new sidewalk.

 

Area of new lawn is 2400 ft²

 

(80-2x)(60-2x) = 2400

4800 - 160x - 120x + 4x² = 2400

4x² - 280x + 2400 = 0

Factor out a 4

x² - 70x + 600 = 0

(x-60)(x-10) = 0

 

x = 60 ft or x = 10 ft

 

Both answers will give an area of 2400 ft²

but with x=60 we have lawn dimensions -60 ft by -40 ft so this is out

 

x = 10 ft width for the sidewalk

 

Check:  New lawn dimensions

(80-2x)(60-2x) = 60(40) = 2400 ft²