Question
Sun August 26, 2012 By:
 

The lengths of the sides forming right angle of a right angled triangle are 5x cm and (3x-1)cm. If the area of the triangle is 60cm sq. find it's hypotenuse.

Expert Reply
Sun August 26, 2012
1/2 bh

1/2 (5x (3x-1)) = 60

1/2 (15x^2 -5x ) = 60

15x^2 - 5x = 120

15x^2 -5x - 120 = 0

3x^2 - x - 24 = 0

3x^2 + 8x - 9x - 24 = 0

x(3x + 8) -3 (3x + 8)

(x-3) (3x + 8)

x = 3 or x = -8/3

since length cannot be -ve

x = 3


so the sides of the triangle are

5(3) and 3(3) - 1 = 15 and 8

By Pythogorean prop

8^2 + 15^2 = hypotenuse ^2

(sum of the squares on the two non - hypotenuse sides is equal to the square on the hypotenuse )

64 + 225 = 289

hypotenuse sqr = 289
hypotenuse = Root of 289

Hyp - 17
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