Question

PLEASE HELP!!! A triangular attic vent has an area of 450 inches squared. The base is 4 times larger than the height.

Write a quadratic equation to model the situation. Let h represent the height.
Solve the equation. Find the base and height of the vent.

Answer 1

The formula for the area of a triangle is 1/2 x base x height.

If we use h to represent the height, then the base must be 4h.

1/2 x base x height = 450

1/2 x 4h x h = 450

2h x h = 450

2h^2 = 450

0 = 2h^2 - 450

0 = h^2 - 225

Equation: h^2 - 225 = 0

OR

(h + 15)(h - 15) = 0

To solve this equation, we can very easily factor it because 225 is a perfect square. When we set each of the factored binomials equal to 0, the answer will be the positive integer. A measurement will never be a negative number.

(h - 15)(h + 15) = 0

h - 15 = 0

h = 15

h + 15 = 0

h = -15

h = 15

Base = 4h = 4 x 15 = 60

Answer:

Base = 60 inches

Height = 15 inches

Hope this helps!