A rectangular carpet 12m long has the same area as a square carpet that has a perimeter of 36m. How wide is the rectangular carpet
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Answer:
if we write the dimensions of rectangular carpet: width -
w
,
height -
h
then we can write, that:
l
=
3
w
−
2
and
w
⋅
(
3
w
−
2
)
=
16
The first equation comes from the sentence: "The length of the rectangular carpet is 2 m less than three times its width." The second comes from the fact that the area of the rectangular and square carpet is equal.
If we expand the equation we get:
3
w
2
−
2
w
−
16
=
0
Δ
=
4
−
4
⋅
3
⋅
(
−
16
)
=
4
+
192
=
196
√
Δ
=
14
w
1
=
2
−
14
6
<
0
We cannot take
w
1
because the dimensions of figures cannot be negative.
w
2
=
2
+
14
6
=
16
6
=
8
3
=
2
2
3
Now if we know, that
w
=
8
3
we can calculate
l
=
3
w
−
2
=
8
−
2
=
6
Answer:
The dimensions are: width -
8
3
m
, height
6
m
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