Math, asked by trishaabhagaat123go, 7 months ago

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

Answered by inglesantos
1

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

Similar questions