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Question
If the difference between the sides of a right-angled triangle is 3 cm and its area is 54 cm2; find its perimeter.
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Solution
Let the two sides be x cm and ( x - 3 ) cm.
Now,
`1/2 xx x xx ( x - 3 )` = 54
x2 - 3x - 108 = 0
( x - 12 )( x + 9 ) = 0
x = 12 cm
Hence the sides are 12 cm, 9 cm and `sqrt( 12^2 + 9^2)` = 15 cm.
The required perimeter is 12 + 9 + 15 = 36 cm.
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