Math, asked by Knhf2455, 11 months ago

The perimeter of a rectangle is 36ft, and the area of the rectangle is 72ft^2 . How do you find the dimensions?

Answers

Answered by finusajid
0

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!

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