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Question
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solution
Using Pythagoras Theorem
`"(hypotenuse)"^2 = sqrt("(height)"^2 + "(base)"^2)`
`AC^2 = sqrt(AB^2 + BC^2)`
`(13)^2 =sqrt( (x )^2 + (x - 7)^2)`
169 = x2 + (x - 7)2
169 = x2 + x2 - 14x + 49
2x2 - 14x - 120 = 0
x2 - 7x - 60 = 0
x2 - 12x + 5x - 60 = 0
x(x - 12) + 5(x - 12) = 0
(x - 12)(x + 5) = 0
Either x - 12 = 0 or x + 5 = 0
x = 12 or x = - 5
Since
Base of right angled triangle = x cm = 12 cm
Right triangle height = x – 7 cm
= 12 - 7
= 5 cm
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