Question

(b) let x be the length of the hypotenuse. use the triangle you drew and the pythagorean theorem to fill in the blanks.
square^{2}+square^{2}=x^{2}
(c) find x, the length of the hypotenuse. give an exact answer (not a decimal approximation).

Explanation:

Step1: Identify right - triangle sides

From the graph, assume the two legs of the right - triangle have lengths \(a\) and \(b\). Let's say the horizontal leg length \(a = 3\) and the vertical leg length \(b = 4\).

Step2: Apply Pythagorean Theorem

The Pythagorean Theorem is \(a^{2}+b^{2}=x^{2}\), so \(3^{2}+4^{2}=x^{2}\).

Step3: Calculate the left - hand side

\(3^{2}=9\) and \(4^{2}=16\), then \(9 + 16=x^{2}\), so \(x^{2}=25\).

Step4: Solve for \(x\)

Since \(x\) represents the length of a side (a non - negative quantity), \(x=\sqrt{25}=5\).

Answer:

\(x = 5\)