Question

18 use the labeled information and the area of the square to find the measure of the hypotenuse in the

answer: m

Explanation:

Step1: Find the side length of the square

The area formula of a square is \(A = s^{2}\), where \(s\) is the side - length. Given \(A = 441m^{2}\), then \(s=\sqrt{441}\).
Since \(21\times21 = 441\), so \(s = 21m\). This side - length is one of the legs of the right - triangle.

Step2: Use the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here \(a = 21m\) and \(b=20m\).
Substitute into the formula: \(c^{2}=21^{2}+20^{2}\).
Calculate \(21^{2}=441\) and \(20^{2} = 400\), then \(c^{2}=441 + 400=841\).
Take the square root of both sides: \(c=\sqrt{841}\).
Since \(29\times29 = 841\), so \(c = 29m\).

Answer:

\(29\)