Question

the frame for the roof of a storage building is shaped like an isosceles right triangle that has a hypotenuse of 16 feet, as shown below. which measurement is closest to x, the length in feet, of each side of the frame? 16√2 8 4 8√2

Explanation:

Step1: Apply Pythagorean theorem

In an isosceles right - triangle, if the legs are of length \(x\) and the hypotenuse \(c = 16\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Since \(a = b=x\), we have \(x^{2}+x^{2}=16^{2}\).

Step2: Simplify the equation

\(2x^{2}=256\). Then \(x^{2}=\frac{256}{2}=128\).

Step3: Solve for \(x\)

\(x=\sqrt{128}\). We can rewrite \(\sqrt{128}\) as \(\sqrt{64\times2}\). Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 64\), \(b = 2\)), we get \(x = 8\sqrt{2}\approx8\times1.414 = 11.312\).
\(16\sqrt{2}\approx16\times1.414 = 22.624\), \(8\) and \(4\) are too small.

Answer:

\(8\sqrt{2}\)