Question

The height of a triangle is 2 feet less than the base. The area of the triangle is 127.5 square feet. Find the length of the base and the height of the triangle.

a) Base = 15 ft, Height = 13.5 ft
b) Base = 14 ft, Height = 12.5 ft
c) Base = 16 ft, Height = 14.5 ft
d) Base = 12 ft, Height = 10.5 ft

Answer 1

The length of the base is 17 feet and the height of the triangle is 15 feet.

Step-by-step explanation:

We can solve this problem by setting up an equation and using the formula for the area of a triangle. Let's represent the base of the triangle as x. Since the height is 2 feet less than the base, we can represent the height as (x - 2). The area of the triangle can be found using the formula A = 1/2 * base * height. Plugging in the values, we have 127.5 = 1/2 * x * (x - 2).

To solve this equation, let's multiply both sides by 2 to get rid of the fraction. We then have 255 = x * (x - 2). Expanding the equation, we get x^2 - 2x - 255 = 0.

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. By factoring, we can rewrite the equation as (x + 15)(x - 17) = 0. This gives us two possible solutions, x = -15 or x = 17. Since the length of the base cannot be negative, we discard -15 as an extraneous solution. Therefore, the length of the base is 17 feet.

To find the height of the triangle, we substitute the value of x into the expression (x - 2). In this case, the height would be (17 - 2) = 15 feet.