Question

The perimeter of a right angle triangle is 30 cm and it's hypotenuse is 13 cm .find the other two side

Answer 1

Sum of other two sides = 30 - 13 = 17 cm

Then, let the sides as ( x ) and ( 17 - x )

By Pythagoras theorem,

( x )² + ( 17 - x )² = 13²

x² + 289 + x² - 34x = 169

2x² + 120 - 34x = 0

x² - 17x + 60 = 0

x² - 12x - 5x +60 = 0

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

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

By Zero Product Rule,

x = 12 [ positive value ]

Other side = 17 - 12 = 5 cm

.

Other sides = 12 cm and 5 cm

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Answer 2

Heya !!

Hypotenuse = 13 cm.

Sum of other two sides of right angled triangle = Perimeter - Hypotenuse = 30 - 13 = 17.

Let One side = X.

Other side = 17-X .

By Pythagoras theorem ,

(13)² = ( X )² + ( 17-X)²

169 = X² + X² + 289- 2×17×Y

169 = 2X² + 289 - 34Y

2X² - 34X + 289 - 169 = 0

2X² - 34X+ 120 = 0

2 ( X² - 17X + 60 ) = 0

X² - 17X + 60 = 0

X² - 12X - 5X + 60 = 0

X ( X - 12 ) - 5 ( X - 12 ) = 0

( X - 12 ) = 0 OR ( X - 5 ) = 0

X = 12 or X = 5.

Hence,

Two other sides are : 12 cm and 5 cm.