Answer:
Height: 16 ft., Base: 18 ft.
Step-by-step explanation:
Let us start with the formula of the area of a triangle, [tex]A=\frac{b*h}{2}[/tex], 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 :
[tex]144=\frac{x(x-2)}{2} \\288=x^2-2x\\x^2-2x-288=0\\(x-18)(x+16)\\x=18,x=-16[/tex]
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 :)
