SOLUTION: The perimeter of a right triangle is 18. If the hypotenuse is 8, how many square units are in the area of the triangle? I know the formula for the area and the perimeter but don't

Algebra ->  Triangles -> SOLUTION: The perimeter of a right triangle is 18. If the hypotenuse is 8, how many square units are in the area of the triangle? I know the formula for the area and the perimeter but don't      Log On


   

Question 181568: The perimeter of a right triangle is 18. If the hypotenuse is 8, how many square units are in the area of the triangle? I know the formula for the area and the perimeter but don't know how to solve for this question with only knowing the hypotenuse.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the legs a and b and the
hypotenuse c
given:
h+%2B+b+%2B+c+=+18
c+=+8
so,
h+%2B+b+%2B+8+=+18
h+%2B+b+=+10
b+=+10+-+h
Now I can say the sides are
h, b+=+10+-+h, and c+=+8
The pythagorean theorem is
h%5E2+%2B+%2810+-+h%29%5E2++=+8%5E2
h%5E2+%2B+100+-+20h+%2B+h%5E2+=+64
2h%5E2+-+20h+%2B+36+=+0
h%5E2+-+10h+%2B+18+=+0
h+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-10
c+=+18
h+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A18+%29%29%2F%282%2A1%29+
h+=+%2810+%2B-+sqrt%28100+-+72%29%29%2F2+
h+=+%2810+%2B-+sqrt%28100+-+72%29%29%2F2+
h+=+%2810+%2B+sqrt%2828%29%29+%2F+2
h+=+%2810+%2B+5.29%29%2F2
h+=+7.65
and
h+=+%2810+-+sqrt%2828%29%29+%2F+2
h+=+%2810+-+5.29%29+%2F+2
h+=+2.35
These 2 values for h turn out to be the legs of the
right triangle, since
h+%2B+b+=+10
7.65+%2B+2.35+=+10
and
h%5E2+%2B+b%5E2++=+8%5E2
7.65%5E2+%2B+2.35%5E2+=+64
58.52+%2B+5.52+=+64
64+=+64
The area is:
A+=+%281%2F2%29%2Ab%2Ah
A+=+%281%2F2%29%2A2.35%2A7.65
A+=+8.99 answer