SOLUTION: The area of a triangle is 39 square ft. The length of one side is 1 ft more than teice the altitude to that side. Find the length of that side and the altitude to the side.

Question 980091: The area of a triangle is 39 square ft. The length of one side is 1 ft more than teice the altitude to that side. Find the length of that side and the altitude to the side.
Found 3 solutions by josgarithmetic, josh_jordan, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
area, ;
a for altitude
b for base length;

The description of the "one side" makes it the base.
.

, so factoring the polynomial will not work.

Discriminant: . PRIME NUMBER.

and the PLUS form is needed.

b=2a+1

Answer by josh_jordan(263)   (Show Source): You can put this solution on YOUR website!
To solve this, we first need to know the formula for the area of a triangle:
, where A is Area, b is base (length of one side), and h is height (altitude)

We are told that the length of one side (base) is 1 ft more than twice the altitude. In other words b = 2h + 1

Now, let's replace b in our formula for the area of a triangle with 2h + 1, and A with 39, since that's the area of the triangle:

We can now solve for h (altitude). First, multiply both sides of this equation by 2, which will give us

(2h + 1)(h) = 39 x 2 -----> (2h + 1)(h) = 78

Next, multiply (2h + 1) by (h), giving us

Third, subtract 78 from both sides and enter a 0 on the right side of the equal sign:

Fourth, factor this quadratic equation, which will give us:

Fifth, set each set of parentheses equal to zero and solve for both values of h:

----->----->

----->

Since the height of a triangle cannot be a negative number, we can discard -13/2. So, our altitude (height) is 6 feet.

To find our length (base), replace the h in 2h + 1 with 6 and compute:

----->----->

Therefore, the length of this triangle is 13 feet and the altitude is 6 feet.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The area of a triangle is 39 square ft. The length of one side is 1 ft more than teice the altitude to that side. Find the length of that side and the altitude to the side.

Altitude: ft
Other side (Base): ft
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