A rectangular Persian carpet has a perimeter of 252 inches. The length of the carpet is 28 in, more than the width. What are the dimensions of the carpet?
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The length of the carpet is 77 inches and the width is 49 inches.
Explanation:
The formula for perimeter is
p
=
2
l
+
2
w
where
p
is the perimeter,
l
is the length and
w
is the width.
If the length of the carpet is 28 in. more than the width we know:
l
=
w
+
28
Substituting
w
+
28
for
l
and 252 for
p
in the formula for perimeter and solving for
w
while keeping the equation balanced gives:
252
=
2
(
w
+
28
)
+
2
w
252
=
2
w
+
56
+
2
w
252
=
4
w
+
56
252
−
56
=
4
w
+
56
−
56
196
=
4
w
196
4
=
4
w
4
w
=
49
And substituting
49
for
w
in the equation for
l
gives:
l
=
49
+
28
l
=
77
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