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

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) (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

John

My calculator said it, I believe it, that settles it

Answer by Gogonati(855) (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:
, where b=5x+3, and h=x, substituting in our formula we get:
solving this equation we get the altitude
, set the equation equal to zero
Solve the equation using quadratic formula

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.
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