The perimeter of a rectangle is 36ft, and the area of the rectangle is 72ft^2 . How do you find the dimensions?
Answers
Answer:
Step-by-step explanation:
The formula for perimeter of a rectangle is
p
=
2
L
+
2
W
. The formula for area is
A
=
L
×
W
Thus,
L
×
W
=
72
,
2
L
+
2
W
=
36
W
=
72
L
→
2
L
+
2
(
72
L
)
=
36
2
L
+
144
L
=
36
2
L
2
L
+
144
L
=
36
L
L
We can now eliminate the denominators since all fractions are equal.
2
L
2
+
144
=
36
L
2
L
2
−
36
L
+
144
=
0
This is a trinomial of the form
y
=
a
x
2
+
b
x
+
c
,
a
≠
1
Therefore, this can be factored by finding two numbers that multiply to
a
×
c
and that add to b, and following the process shown below. These two numbers are
− 12 and − 24 2 L 2 − 12 L − 24 L + 144 = 0 2 L ( L − 6 ) − 24 ( L − 6 ) = 0 ( 2 L − 24 ) ( L − 6 ]= 0 L = 12 and 6
Since the length can be the width and vice-versa, the sides of the rectangle measure 12 and 6.
Hopefully this helps!