Question

1. find the unknown side of the triangle when x = 24 in and y = 7 in. use the pythagorean theorem to solve for the hypotenuse (c²).

a. 625 in
b. 25 in
c. 576 in
d. 49 in

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(c^{2}=x^{2}+y^{2}\), where \(x\) and \(y\) are the legs of the right - triangle and \(c\) is the hypotenuse. Given \(x = 24\) in and \(y=7\) in.

Step2: Substitute values into the formula

Substitute \(x = 24\) and \(y = 7\) into the formula \(c^{2}=x^{2}+y^{2}\). We know that \(x^{2}=24^{2}=24\times24 = 576\) and \(y^{2}=7^{2}=7\times7 = 49\). Then \(c^{2}=576 + 49\).

Step3: Calculate the sum

Calculate \(576+49=625\), so \(c^{2}=625\). Then, to find \(c\), we take the square root of both sides. Since \(c\) represents the length of a side of a triangle, we take the positive square root. \(\sqrt{c^{2}}=\sqrt{625}\), so \(c = 25\) in.

Answer:

b. 25 in