Question

A rectangular lawn measures 80 ft by 120 ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new lawn is 3200 ft2. How wide is the​ sidewalk? The sidewalk is nothing ▼ ft squared ft cubed ft wide.

Answer 1

Both of them give the same answer

Answer 2

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 ft^2

Explanation:

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 ft^2

(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