The perimeter of a rectangle is 62 m. Find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

Question

Mauricio

Mathematics

25 October, 17:34

The perimeter of a rectangle is 62 m. Find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

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Answers (1)

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Felipe Ward · Answer 1

22m by 9m.

Step-by-step explanation:

1980000 cm^2 = 1980000 / 1000 = 198 m^2.

If the length is L and the width is W, then

2L + 2W = 62

LW = 198

L = 198 / W

Substitute for L in the first equation:

2W + 2 (198/W) = 62

Multiply through by W:

2W^2 + 396 = 62W

2W^2 - 62W + 396 = 0

W^2 - 31W + 198 = 0

(w - 22) (W - 9) = 0

so W = 22 or 9.

when W = 22. L = 198/W = 9

As L is the longest side L = 22 and W = 9m.