A border of uniform width is built around a rectangular garden that measures 19 ft by 36 ft. (see Illustration). The area of the border is 804 ft ². Find the width of the border, y. A) 7 ft B) 4 ft C) 6 ft D) 5 ft E) 37 ft

Question

Quizplus · Accepted Answer

Let the width of the border be y feet.
Then the width of the inner rectangle is 19-2y and the length is 36-2y.
The outer dimensions of the whole garden are (19+2y) and (36+2y).
The area of the border is the difference between the area of the outer rectangle and the area of the inner rectangle:
(19+2y)(36+2y) - 19*36 = 804
Simplifying and solving for y, we get:
4y^2 + 70y - 585 = 0
Using the quadratic formula, we get:
y = (-70 ± sqrt(70^2 + 4*4*585))/8
y = (-70 ± 74)/8
y = -18/4 or y = 1.5
Since the width of the border cannot be negative, we take y = 1.5.
Therefore, the width of the border is 6 feet (since y is the width on both sides of the rectangle). Choice C is the best choice.

A Border of Uniform Width Is Built Around a Rectangular