The base of the triangle is 1 meter less than the height. The area is 15 meter squared. What is the height of the triangle

Question

The base of the triangle is 1 meter less than the height. The area is 15 meter squared. What is the height of the triangle?

Answer 1

Let H = height of the triangle

Area of a Triangle = (1/2) (BASE) (HEIGHT)

15 = (1/2) (H - 1) (H)

15 = (1/2) (H^2 - H) Multiplying H times (H - 1).

30 = H^2 - H Multiplying both sides of the equation by 2 to get rid

of the fraction 1/2.

0 = H^2 - H - 30 Subtracting 30 from both sides of the equation.

0 = (H - 6) (H + 5) Factoring

Therefore, H - 6 = 0 and H + 5 = 0, and H = 6 and H = -5.

But, we eliminate the -5, since the height is not a negative number here.

ANSWER: HEIGHT OF THE TRIANGLE IS 6 METERS.

CHECKING:

DOES 15 = (1/2) (6 - 1) (6)?

(1/2) (5) (6) = (1/2) (30) = 15 Yes!

Hope this was helpful An A.