SOLUTION: I need some help figuring out how to do this word problem. The base of a triangle is 6cm greater than the height. The area is 36cm^2. How do you find the height and length of the b

Algebra ->  Equations -> SOLUTION: I need some help figuring out how to do this word problem. The base of a triangle is 6cm greater than the height. The area is 36cm^2. How do you find the height and length of the b      Log On


   

Question 318542: I need some help figuring out how to do this word problem. The base of a triangle is 6cm greater than the height. The area is 36cm^2. How do you find the height and length of the base>
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = the base
Let h = the height
A+=+%281%2F2%29%2Ab%2Ah
given:
b+=+h+%2B+6 cm
A+=+36 cm2
---------------
36+=+%281%2F2%29%2Ab%2Ah
36+=+%281%2F2%29%2A%28h+%2B+6%29%2Ah
36+=+%281%2F2%29%2A%28h%5E2+%2B+6h%29
Multiply both sides by 2
72+=+h%5E2+%2B+6h
h%5E2+%2B+6h+-+72+=+0
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+6
c+=+-72
h+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-72%29+%29%29%2F%282%2A1%29+
h+=+%28-6+%2B-+sqrt%28+36+%2B+288+%29%29%2F2+
h+=+%28-6+%2B-+sqrt%28+324+%29%29%2F2+
h+=+%28-6+%2B+18%29%2F2 (can't use the negative square root)
h+=+12%2F2
h+=+6
and, since
b+=+h+%2B+6
b+=+12
The height is 6 cm and the base is 12 cm
check:
A+=+%281%2F2%29%2A12%2A6
A+=+%281%2F2%29%2A72
A+=+36 cm2
OK