SOLUTION: the area of a triangular sheet of paper is 13 square inches. one side of the triangle is 3 inches more than five times the length of the altutude to that side. find the length of t

Algebra ->  Triangles -> SOLUTION: the area of a triangular sheet of paper is 13 square inches. one side of the triangle is 3 inches more than five times the length of the altutude to that side. find the length of t      Log On


   

Question 513743: the area of a triangular sheet of paper is 13 square inches. one side of the triangle is 3 inches more than five times the length of the altutude to that side. find the length of that side and the altitude to that side
Found 2 solutions by solver91311, Gogonati:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the measure of the altitude. Then the measure of the side related to that altitude is . Since we know the area of a triangle is the measure of the base times the measure of the altitude to that base divided by 2, we can write:



Which is to say:



Solve the quadratic for , discard the extraneous negative root, then calculate

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Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Lets the altitude = x inches, then the side will be 5x+3 inches.
As we know the area of triangle is given by the formula:
A=%28b%2Ah%29%2F2, where b=5x+3, and h=x, substituting in our formula we get:
+13=x%2A%285x%2B3%29%2F2 solving this equation we get the altitude
26=5x%5E2%2B3x, set the equation equal to zero
5x%5E2%2B3x-26=0Solve the equation using quadratic formula
x=-3%2B-sqrt%283%5E2-4%2A5%2A%28-26%29%29%2F%282%2A5%29
x=2 (The negative root is rejected)
To find the length of the side plug x=2, and get b=5*2+3=13
Answer:The length is 13 inches and the altitude to this side is 2 inches.