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


Best Answer

Solution:

From Pythagoras theorem,

Base2 + Altitude2 = hypotenuse2

x2 + (x – 7)2 = 132

= x2 + x2 +49 – 14x  = 169

= 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, i.e., x = 12 or x = −5

Since sides are positive, x can only be 12.

Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 − 7) cm = 5 cm.

 

 

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