Question

1. 48.5 ft 32.5 ft 39 ft (triangle diagram)

Explanation:

Assuming the problem is to verify if it's a right triangle (using Pythagorean theorem) or find an unknown side/area. Let's check the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse.

Step1: Identify sides

Let \(a = 39\), \(b = 32.5\), \(c = 48.5\).

Step2: Calculate \(a^2 + b^2\)

\(39^2 + 32.5^2 = 1521 + 1056.25 = 2577.25\)

Step3: Calculate \(c^2\)

\(48.5^2 = 2352.25\)? Wait, no, \(48.5^2=(48 + 0.5)^2 = 48^2 + 2480.5 + 0.5^2 = 2304 + 48 + 0.25 = 2352.25\)? Wait, but \(39^2 + 32.5^2 = 1521 + 1056.25 = 2577.25\), and \(48.5^2 = 2352.25\)? That can't be. Wait, maybe I miscalculated. Wait, \(32.5^2 = (65/2)^2 = 4225/4 = 1056.25\), \(39^2 = 1521\), sum is \(1521 + 1056.25 = 2577.25\). \(48.5^2 = (97/2)^2 = 9409/4 = 2352.25\). Wait, that's not equal. Wait, maybe the problem is to find the area? Area of triangle is \(\frac{1}{2} \times base \times height\). Let's take base = 39, height = 32.5.

Step4: Calculate area

\(\frac{1}{2} \times 39 \times 32.5 = \frac{39 \times 32.5}{2}\)
\(39 \times 32.5 = 39 \times \frac{65}{2} = \frac{2535}{2} = 1267.5\)
Then \(\frac{1267.5}{2} = 633.75\) square feet.

Answer:

If the problem is area, the answer is \(633.75\) square feet. If verifying Pythagorean theorem, \(39^2 + 32.5^2
eq 48.5^2\) (wait, maybe I made a mistake: \(48.5^2 = (48 + 0.5)^2 = 48^2 + 48 + 0.25 = 2304 + 48 + 0.25 = 2352.25\), \(39^2 + 32.5^2 = 1521 + 1056.25 = 2577.25\), which is not equal. Wait, maybe the hypotenuse is 48.5, and we check the other side. Wait, \(c^2 - b^2 = 48.5^2 - 32.5^2 = (48.5 - 32.5)(48.5 + 32.5) = 16 \times 81 = 1296\), and \(\sqrt{1296} = 36\), but the base is 39. So maybe the problem is to find the area, so using base 39 and height 32.5, area is \(\frac{1}{2} \times 39 \times 32.5 = 633.75\) square feet.