Question

$\huge \fbox \red{❥ Question}$

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides?
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Answer 1

Answer:

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☘ Let base be x cm , then altitude will be (x-7) cm.

Now ,

By using pythagoras theorem-

132 = x2 + (x-7)2

169 = x2 + x2 + 49 - 14x

2x2 - 14x - 120 = 0

x2 - 7x - 60 = 0

x2 - 12x + 5x - 60 = 0

x ( x - 12 ) + 5 ( x - 12 ) = 0

Hence x = 12

so , Altitude is 5 cm

and base = 12cm

Answer 2

$\huge \fbox \red{❥ Answer}$

Let x be the base of the triangle, then the altitude will be (x−7).

By Pythagoras theorem,

x²+(x−7)²=(13)²

2x²−14x+49−169=0

2x²−14x−120=0

x²−7x−60=0

x²−12x+5x−60=0

(x−12)(x+5)=0

x=12,x=-5.

Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be 12−7=5cm.

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