Question

The area of right triangle is 40 and its perimetre is 40 .length of hypotenuse

Answer 1

Heya

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Let the length of hypotenuse , base and altitude be h , b and L

It's perimeter = h + L + b

And

it's Area = 1/2 ( b × L )

ACCORDING TO THE QUESTION

L + h + b = 40

And

1/2 ( L × b ) = 40

L × b = 80

WE KNOW THAT A.M ≥ G.M

( L + b ) / 2 ≥ ( 80 )½

=>

L + b = 2 × 2 √20

L + b = 4√20

=>

4√20 + h = 40

h = 40 - 4√20

=>

h = 4 ( 10 - √20 ) units.

Answer 2

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