Question

The height of a triangle is 2ft less than the base x. The area is 144ft2

Answer 1

Height: 16 ft., Base: 18 ft.

Explanation:

Let us start with the formula of the area of a triangle,
`A=(b*h)/(2)`, where b represents the base of the triangle, and h represents the height of the triangle.

In this problem, we will set the base of the triangle as x. The height is 2 ft. less than the base, and thus would have the expression, x-2. Let us plug the values into our formula to solve for x :

`144=(x(x-2))/(2) \\288=x^2-2x\\x^2-2x-288=0\\(x-18)(x+16)\\x=18,x=-16`

Since we set x as the base of the triangle, we now know that the base of the triangle is 18 ft. because the the base cannot have a negative length.The height would then be x-2, so 16 ft.

I hope this helps! Let me know if you have any questions :)