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.

Answer 1

Answer:

base = 12 cm , altitude = 5 cm

Step-by-step explanation:

Let the base of right

triangle = x cm

Altitude of the triangle = (x-7)cm

Hypotenuse = 13 cm ( given )

By Phythogarian theorem,

(Hypotenuse)² = (base)²+(altitude)²

=> ( 13 )² = x² + ( x - 7 )²

=> 169 = x² + x² - 2.x.7 + 7²

=> 169 = 2x² - 14x + 49

=> 169 - 49 = 2x² - 14x

=> 120 = 2x² - 14x

Divide each term by 2 , we get

=> 60 = x² - 7x

=> x² - 7x - 60 = 0

=> x² - 12x + 5x - 60 = 0

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

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

x - 12 = 0 or x + 5 = 0

x = 12 or x = -5

x should not be negative.

Therefore ,

x = 12

Now ,

Base of the triangle = x = 12 cm

Altitude = ( x - 7 )

= 12 -. 7

= 5 cm

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