Question

A rectangular garden has a width that is
8
feet less than the length,
x
. The area of the garden is
240
square feet.



Which of the following equations can be used to find the length of the garden, and what is the solution for
x
?



A.
x
(
x
−
8
)
=
240

x
=
12
feet

B.
x
(
x
−
8
)
=
240

x
=
20
feet

C.
x
(
x
+
8
)
=
240

x
=
12
feet

D.
x
(
x
+
8
)
=
240

x
=
20
feet

Answer 1

Width = x − 8, area = length × width → x(x − 8) = 240.
Solve: x^2 − 8x − 240 = 0. Discriminant = 64 + 960 = 1024, √ = 32.

x = (8 ± 32)/2 → x = 20 or x = −12 (reject). So x = 20 ft.

Answer: B.