Question

Algebra Word Problems:

1. The length of the floor of a one-storey building is 14 feet longer than its width. The building has 1,632 square feet of floor space. Write a quadratic equation for the area of the floor in terms of w. Find the length and width of the floor.

2. A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens. The gardener wants the enclosed area to be 400 square meters. What dimensions should the gardener use to obtain this area?

Answer 1

1.
width --- w
length -- w+14

w(w+14) = 1632
w^2 + 14w = 1632
w^2 + 14w + 49 = 1632 + 49
I completed the square
(w+7)^2 = 1681
w+7 =±41
w = -7 ± 41 = 34 or a negative

the width is 34 ft and the length is 48 ft

or

it factors to
(x-34)(x+48) = 0
x = 34 or x = -48

2.
width ---- x
lengty --- y
2x + 2y = 100
x+y = 50
y = 50-x

area = 400
xy = 400
x(50-x) = 400
50x - x^2 - 400 = 0
x^2 - 50x + 400 = 0
x^2 - 50x = -400
x^2 - 50x + 625 = -400 + 625
(x-25)^2 = 225
x-25 = ± 15
x = 25 ± 15

x = 40 or x = 10

if x = 40, y = 10
if x = 10, y = 40

the garden should be 10 m by 40 m