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Question
The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.
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Solution
Let one hypotenuse of the triangle be x cm.
From the given information,
Length of one side = (x – 1) cm
Length of other side = (x – 18) cm
Using Pythagoras theorem,
x2 = (x – 1)2 + (x – 18)2
x2 = x2 + 1 – 2x + x2 + 324 – 36x
x2 – 38x + 325 = 0
x2 – 13x – 25x + 325 = 0
x(x – 13) – 25(x – 13) = 0
(x – 13)(x – 25) = 0
x = 13, 25
When x = 13, x – 18 = 13 – 18 = –5, which being negative, is not possible.
So, x = 25
Thus, the lengths of the sides of the triangle are x = 25 cm, (x – 1) = 24 cm and (x – 18) = 7 cm.
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