SOLUTION: I am trying to find the answer to the following: a. Using the pythagorean theorem, find the perimeter of triangle ABC if the hypotenuse is AB is 20 and the base CB is 16. (heigh

Algebra ->  Pythagorean-theorem -> SOLUTION: I am trying to find the answer to the following: a. Using the pythagorean theorem, find the perimeter of triangle ABC if the hypotenuse is AB is 20 and the base CB is 16. (heigh      Log On


   

Question 125342: I am trying to find the answer to the following:
a. Using the pythagorean theorem, find the perimeter of triangle ABC if the hypotenuse is AB is 20 and the base CB is 16. (height AC is unknown)
b. Using the pythagorean theorem, find the area of triangle ABC using the information from a above.


Found 3 solutions by josmiceli, Earlsdon, cmerrill666:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
20%5E2+=+16%5E2+%2B+h%5E2
400+=+256+%2B+h%5E2
h%5E2+=+400+-+256
h+=+sqrt%28144%29
h+=+12
perimeter = 12 + 16 + 20
perimeter = 48
---------------
A+=+%281%2F2%29%2Ab%2Ah
A+=+%281%2F2%29%2A16%2A12
A+=+96

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem to find the height of a right triangle if the hypotenuse is 20 and the base is 16.
c%5E2+=+a%5E2%2Bb%5E2 Substitute c = 20, a = 16, and b = h
20%5E2+=+16%5E2%2Bh%5E2
400+=+256+%2B+h%5E2 Subtract 256 from both sides.
144+=+h%5E2 Take the square root of both sides.
12+=+h We discard the negative answer because the height of a triangle is positive.
So the triangle has side: 20, 16, and 12
a) The perimeter is:
P+=+20%2B16%2B12
P+=+48
b) The area is:
A+=+%281%2F2%29bh Substitute b = 16 and h = 12.
A+=+%281%2F2%29%2816%29%2812%29
A+=+96sq. units.

Answer by cmerrill666(3) About Me  (Show Source):