The hypotenuse of a right angled triangle is 4cm more than thrice the shorter side. If the third side is 1cm less than the hypotenuse, find the sides of the triangle.

Asked by Sneha George | 27th Feb, 2011, 12:00: AM

Expert Answer:

Dear student,
 
Let the length of the shorter side be x. Therefore,
Hypotenuese = 4 + 3x
Length of third side = 4 + 3x - 1 = 3 + 3x
Using Pythagoras theorem, we have:
(4 + 3x)2 = (3 + 3x)2 + x2
16 + 9x2 + 24x = 9 + 9x2 + 18x + x2
16 + 24x = 9 + 18x + x2
x2 - 6x - 7 = 0
x2 + x - 7x - 7 = 0
x(x + 1) - 7(x + 1) = 0
(x - 7) (x + 1) = 0
x = 7 or x = -1
But, x cannot be negative. So, x = 7
 
Thus, the lengths of the three sides of the right triangle are 7 cm, 25 cm and 24 cm.
 
 
We hope that clarifies your query.
 
Regards,
Team
TopperLearning

Answered by  | 27th Feb, 2011, 01:03: PM

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