Answer:
14 ft
Step-by-step explanation:
Focus on the triangle, and temporarily neglect the 2 ft measurement at the top of the triangle. Then the 2 legs of the triangle have lengths h - 2 ft and 5 ft, and the hypotenuse is 13.
Applying the Pythagorean Theorem, we get:
13^2 = (h - 2)^2 + 5^2, or
169 = h^2 - 4h + 4 + 25, or
144 = h^2 - 4h + 4, or
140 = h^2 - 4h, or, finally,
h^2 - 4h - 140 = 0. We must find the value of h.
I graphed this function on a calculator and found that -10 is a zero. Thus, the function factors into (h + 10)(h - 14) = 0, or h = 14.
The total height of the piece of plywood is 14 ft.
Check this: does a right triangle with legs (14 - 2) and 5 have a hypotenuse of 13? Yes.
