Question for Solving Equations by Taking Square Roots

Question

A lot for sale is shaped like a trapezoid. The bases of the trapezoid represent the widths of the front and back yards. The width of the back yard is twice the width of the front yard. The distance from the front yard to the back yard, or the height of the trapezoid, is equal to the width of the back yard. Find the width of the front and back yards, given that the area is 4,200 square feet. Round to the nearest foot.

Answer 1

Hi Othman,

Let's use the variable, w, to represent the width of the front yard.

Since the width of the backyard is twice that of the front, the following expression will represent the width of the back yard: 2w

Since the height of the trapezoid is equal to the width of the backyard , the following expression will represent the height: 2w

The area of a trapezoid can be determined by:

A =(b1 + b2 ) • h

2

Let's substitute the expressions from the info above and determine the value of w by solving the equation:

4200 = (w + 2w) • 2w

2

4200 • 2= (w + 2w) • 2w •2

2

8400 = (w + 2w) • 2w

8400 = 3w • 2w

8400 = 6w²

8400/6 = 6w² / 6

1400 = w²

37.4 ft = w ( THE WIDTH OF THE FRONT YARD)

The backyard will be 2w or 2 • 37.4 = 74.8 ft

Rounding to the nearest whole number will give us:

Width of front yard = 37 feet

Width of backyard = 75 feet