SOLUTION: express the hypotenuse h of a right triangle with area 25m^ as a function of its perimeter p (take base and height as a and b)

Algebra ->  Pythagorean-theorem -> SOLUTION: express the hypotenuse h of a right triangle with area 25m^ as a function of its perimeter p (take base and height as a and b)      Log On


   

Question 785524: express the hypotenuse h of a right triangle with area 25m^ as a function of its perimeter p (take base and height as a and b)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a= length of one leg, in meters
b= length of the other leg, in meters
h= hypotenus of the triangle, in meters
ab%2F2=25= area of the triangle, in square meters
p=a%2Bb%2Bh= perimeter of the triangle, in square meters

ab%2F2=25-->ab=25%2A2-->ab=50
p=a%2Bb%2Bh-->p-h=a%2Bb
According to the Pythagorean theorem:
h%5E2=a%5E2%2Bb%5E2
p%5E2=%28a%2Bb%2Bh%29%5E2=a%5E2%2Bb%5E2%2Bh%5E2%2B2ab%2B2ah%2B2bh
p%5E2-h%5E2=h%5E2%2B2ab%2B2ah%2B2bh
p%5E2-h%5E2=h%5E2%2B2%2A50%2B2ah%2B2bh (substituting ab=50)
p%5E2=2h%5E2%2B100%2B2ah%2B2bh
p%5E2=2h%5E2%2B100%2B2h%28a%2Bb%29
p%5E2=2h%5E2%2B100%2B2h%28p-h%29 (substituting p-h=a%2Bb)
p%5E2=2h%5E2%2B100%2B2hp-2h%5E2
p%5E2=100%2B2hp
p%5E2-100=2hp
highlight%28h=%28p%5E2-100%29%2F2p%29
or something equivalent, like
highlight%28h=p%2F2-50%2Fp%29 or highlight%28h=%28p%2B10%29%28p-10%29%2F2p%29

EXTRA:
A more general expression, bases on perimeter and area A would be
highlight%28h=%28p%5E2-4A%29%2F2p%29