Question

kimmy is drawing a right triangle with chalk on the outside pavement. the first side of the triangle measures 14 feet, and the second side of the triangle is the longest side, measuring 22 feet. how long is the third side of the triangle, in feet? round your answer to two decimal places. show your work here hint: to add the square root symbol (√), type
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (longest side). Let \(a = 14\) and \(c = 22\). We need to find \(b\).

$$b^{2}=c^{2}-a^{2}$$

Step2: Substitute values

Substitute \(a = 14\) and \(c = 22\) into the formula:

$$b^{2}=22^{2}-14^{2}$$

$$b^{2}=484 - 196$$

$$b^{2}=288$$

Step3: Solve for \(b\)

$$b=\sqrt{288}$$

$$b=\sqrt{144\times2}$$

$$b = 12\sqrt{2}\approx12\times1.414 = 16.97$$

Answer:

\(16.97\)