SOLUTION: THE ALTITUDE OF RIGHT ANGLE TRIANGLE IS 7 cm LESS THAN ITS BASE.IF THE HYPOTENUSE IS 13 cm,FIND THE OTHER TWO SIDES

Question 752607: THE ALTITUDE OF RIGHT ANGLE TRIANGLE IS 7 cm LESS THAN ITS BASE.IF THE HYPOTENUSE IS 13 cm,FIND THE OTHER TWO SIDES

Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
let base of triangle is x cm
altitude will be x-7
hypotenuse =13 given
H^2 =x^2+(x-7)2 by Pythagoras theorm
13^2 =x^2 +(x-7)^2
169=x^2+x^2+49-14x
169=2x^2-14x+49
2x^2-14x-120 =0
x^2-7x-60
by splitting middle term
x^2-12x+5x-60 =0
(x-12)(x+5) =0
x-12 =0 or x+5=0
x=12 or x=-5
neglecting negative value
x=12 cm
there for base is 12cm
and altitude is 12-7 =5cm
ANSWER base is 12 cm
altitude 5 cm

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