SOLUTION: The area of a triangular sheet of paper is 190 square inches. One side of the triangle is 8 inches more than three times the length of the altitude to that side. Find the length of

Algebra ->  Triangles -> SOLUTION: The area of a triangular sheet of paper is 190 square inches. One side of the triangle is 8 inches more than three times the length of the altitude to that side. Find the length of      Log On


   

Question 358440: The area of a triangular sheet of paper is 190 square inches. One side of the triangle is 8 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.
Found 2 solutions by mananth, edjones:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a triangular sheet of paper is 190 square inches. One side of the triangle is 8 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.
..
let altitude be x
the base = 3x+8
Area = 190 m^2
...
1/2 * x * (3x+8) = 190
multiply by 2
x(3x+8)=190*2
3x^2+8x=380
3x^2+8x-380=0
use the quadratic equation to find the roots x1 & x2
b^2-4ac = 4624
x1=(-8+sqrt(4624))/2
x1=10 inches the altitude
x2 =negative so ignore
base = 3*10+8 = 38 inches
...
m.ananth@hotmail.ca

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let a=altitude
.5a(3a+8)=190
a(3a+8)=380
3a^2+8a-380=0
-380*3=-1140
factors of 1140 whose sum is 8 are 38 and -30
3a^2-30a+38a-380
=3a(a-10)+38(a-10)
=(3a+38)(a-10)
a=10"
.
Ed