Question

the perimeter of a right angle is 60 cm and its hypotenuse is 25 cm find the area of triangle

Answer 1

Perimeter of right angled triangle = length of 1st side + length of 2nd side + length of hypotenuse

60 cm = length of 1st side + length of 2nd side + 25 cm

60 cm - 25 cm = ;ength of 1st side + length of 2nd side

35 cm = length of 1st side + length of 2nd side

35 cm - length of 1st side = length of 2nd side    ...( i )

Now,

     By Pythagoras Theorem      

⇒ ( length of 1st side )^2 + ( length of 2nd side )^2 = ( hypotenuse )^2

⇒ ( length of 1st side )^2 + ( 35 cm - length of 1st side )^2 = ( 25 cm )^2

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( a - b )^2 = a^2 + b^2 - 2ab

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⇒ ( length of 1st side )^2 + 1225 cm^2 + ( length of 1st side )^2 - 70( length of 1st side ) = 625 cm^2

⇒ 2( length of 1st side )^2 - 70( length of 1st side ) + 1225 cm^2 - 625 cm^2 = 0

⇒ 2( length of 1st side )^2 - 70( length of 1st side ) +  600 cm^2 = 0  

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length of 1st side is written as x for convenience.

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⇒ 2x^2 - 70x + 600 = 0

⇒ x^2 - 35x + 300 = 0

⇒ x^2 - ( 15 + 20 )x + 300 = 0

⇒ x^2 - 15x - 20x + 300 = 0

⇒ x( x - 15 ) - 20( x - 15 ) = 0

⇒ ( x - 15 )( x - 20 ) = 0

⇒ x = 15 or  x = 20

⇒ Length of 1st side  = 15 or 20

If we subtract 15 from 35, we will get 20 . if we subtract 20 from 35 , we will get 15. So, we can say that the sides are 15 and 20.

Therefore, 1st and 2nd sides are 15 cm and 20 cm.As it is a right angled triangle.

Area = 1 / 2 × length of 1st side × length of 2nd side

Area = 1 / 2 × 15 cm × 20 cm

Area = 15 cm × 10 cm

Area of the right angled triangle is 150 cm^2.

Answer 2

HEY MATE HERE IS YOUR ANSWER

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