Question

The perimeter of a right angle triangle is 144 cm and its hypotenuse side is 65 cm. So, find the other 2 sides of triangle.


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Answer 1

Answer:

63 cm  and 16 cm

Step-by-step explanation:

Given :

Perimeter of the right angled triangle = 144 cm .

Hypotenuse is given 65 cm .

Let the sides be x , y and z .

x = height .

y = base .

z = hypotenuse.

By Pythagoras theorem :

z² = y² + x²

⇒ ( 65 )² = y² + x²

⇒ 4225 = y² + x²

⇒ x² + y² = 4225 ..........( 1 )

Now perimeter = 144 cm

⇒ x + y + z = 144

⇒ x + y + 65 = 144

⇒ x + y = 144 - 65

⇒ x + y = 79

⇒ x = 79 - y .,................( 2 )

Put this equation 1 :

( 79 - y )² + y² = 4225

Use ( a - b )² = a² + b² - 2 ab

⇒ 79² + y² - 158 y + y² = 4225

⇒ 6241 + 2 y² - 158 y - 4225 = 0

⇒ 2016 + 2 y² - 158 y = 0

⇒ 2 y² - 158 y + 2016 = 0

⇒ y² - 79 y + 1008 = 0

⇒ y² - 63 y - 16 y + 1008 = 0

⇒ y ( y - 63 ) - 16 ( y - 63 ) = 0

⇒ ( y - 63 )( y - 16 ) = 0

By zero product rule :

either y = 63

or y = 16

x + y = 79.

So x = 63 or 16 .

ANSWER:

The two sides are 63 and 16 cm

Answer 2

ANSWER

16,63



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