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A room has an area of 60 square meters and a perimeter of 32 meters. What are the length and width of the room?

A room has an area of 60 square meters and a perimeter of 32 meters What are the length and width of the room class=

Respuesta :

choixongdong
L x W = 60
2(L + W) = 32
 L + W = 16
 L = 16 - W

substitute  L = 16 - W into L x W = 60
L x W = 60
(16 - W) x W = 60
16W -W^2 = 60
W^2 - 16W + 60 = 0
(W - 6)(W - 10) = 0
W - 6 = 0; W = 6
W - 10 = 0; W = 10

answer
Length = 10 m and Width = 6 m

The length of the room  is  10 m and width is 6m.

We have given that the area is 60 square meters

and perimeter of the square is 32 meters

What is the formula for the area of the square?

[tex]Area =L \times W[/tex]

we have given that the area is 60

Therefore,[tex]L \times W = 60.......(1)[/tex]

What is the formula for the perimeter?

[tex]Perimeter=2(L + W)[/tex]

From given we get,

[tex]2(L + W) = 32[/tex]

[tex]L + W = 16[/tex]

[tex]L = 16 - W.......(2)[/tex]

Substitute the value of  L = 16 - W into (1) we get,

[tex]L \times W = 60[/tex]

[tex](16 - W) \times W = 60[/tex]

[tex]16W -W^2 = 60[/tex]

[tex]W^2 - 16W + 60 = 0[/tex]

[tex](W - 6)(W - 10) = 0[/tex]

[tex]W - 10 = 0\implies W = 10\\W - 6 = 0\implies W = 6[/tex]

Therefore the length is  10 m and width is 6m.

To learn more about the square visit:

https://brainly.com/question/25092270

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