The perimeter of a right angle triangle is 30 cm and it's hypotenuse is 13 cm .find the other two side
jsdcorreo:
5 cm and 12 cm, http://triancal.esy.es/?g=3&c=13&p=30
Answers
Answered by
6
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
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
Answered by
5
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.
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.
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