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:
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