A wire of length 150 cm is bent into a rectangle. If the length of the rectangle is 5 cm less than thrice its breadth, then answer the following: The length of the rectangle is _ cm. The breadth of the rectangle is _ cm.
Answers
Step-by-step explanation:
The length of the rectangle is 5cm less than thrice its width. Find the dimensions of the rectangle if its area is 112cm²?
Algebra Linear, Exponential, and Quadratic Models
1 Answer
Stefan V.
Sep 6, 2015
Length:
16 cm
Width:
7 cm
Explanation:
First, start by writing the formula for the area of a rectangle of width
w
and length
l
A
=
l
⋅
w
Now, you know that if you triple the rectangle's width and subtract 5 cm from the result, you get the rectangle's length.
This means that you can write
l
=
3
⋅
w
−
5
Since you know that the area of the rectangle is equal to
112 cm
3
, you can write a second equation using
l
and
w
(
3
w
−
5
)
⋅
w
=
112
3
w
2
−
5
w
=
112
3
w
2
−
5
w
−
112
=
0
Use the quadratic formula to find the two solutions to this quadratic equation
w
1
,
2
=
(
(
−
5
)
)
±
√
(
−
5
)
2
−
4
⋅
3
⋅
(
−
112
)
2
⋅
3
w
1
,
2
=
5
±
√
1369
6
w
1
,
2
=
5
±
37
6
Since
w
represents the width of the rectangle, the negative solution will have no physical significance. This means that the only valid solution to this quadratic is
w
=
5
+
37
6
=
42
6
=
7 cm
The length of the rectangle will be
3
⋅
7
−
5
=
21
−
5
=
16 cm