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) (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:
(1)
The diagonal of the room is the square root of 1312:
(2)
To solve the system of equations (1) and (2), first square (1):
(3)
Then subtract (2) from (3):
(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.
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