SOLUTION: Liboko builds a rectangular storeroom. If the diagonal of the room is √1312 m and the perimeter is 80 m , determine the dimensions of the room.

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Question 1092306: Liboko builds a rectangular storeroom. If the diagonal of the room is √1312 m and the perimeter is 80 m , determine the dimensions of the room.
Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!

Let x and y be the length and width of the room.

The perimeter is 80:
2x%2B2y+=+80
x%2By+=+40 (1)

The diagonal of the room is the square root of 1312:
sqrt%28x%5E2%2By%5E2%29+=+sqrt%281312%29
x%5E2%2By%5E2+=+1312 (2)

To solve the system of equations (1) and (2), first square (1):
x%5E2+%2B+2xy+%2B+y%5E2+=+1600 (3)

Then subtract (2) from (3):
2xy+=+288
xy+=+144 (4)

You could solve (1) and (4) algebraically; but it's faster just to look for a pair of numbers whose sum is 40 and whose product is 144. Those numbers are 36 and 4.

Liboko has a very long and narrow storeroom with length 36m and width 4m.