SOLUTION: The area of a triangular sheet of paper is 28 square inches. One side of the triangle is 2 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 28 square inches. One side of the triangle is 2 inches more than three times the length of the altitude to that side. Find the length of       Log On


   

Question 339749: The area of a triangular sheet of paper is 28 square inches. One side of the triangle is 2 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to that side. Can you please set the solution in a step by step method. Thank you for your help.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let altitude be x
base = 3x+2..
Area of triangle = %281%2F2%29+%2A+base%2Aaltitude
28 = %281%2F2%29%2Ax%2A%283x%2B2%29
multiply by 2
2*28= x%2A%283x%2B2%29
56=3x^2+2x
add -56 to both sides
56-56=3x^2+2x-56
3x^2+2x-56=0
solve using quadratic formula
x=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
a=3, b=2,c =-56
x1=%28-2%2Bsqrt%282%5E2-4%2A3%2A%28-56%29%29%29%2F%286%29
x1=4 inches
x1=%28-2-sqrt%282%5E2-4%2A3%2A%28-56%29%29%29%2F%286%29
x2=-4.66
ignore negative value.
Altitude = 5
base = 3x+2 = 15+2 =17 inches