Question

melvin is drawing a right triangle with chalk on the outside pavement. the first side of the triangle measures 15 feet, and the second side of the triangle is the longest side, measuring 25 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 the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side). Let \(a = 15\) (one leg) and \(c = 25\) (the hypotenuse). We need to find \(b\). Rearranging the formula for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 15\) and \(c = 25\) into the formula: \(b=\sqrt{25^{2}-15^{2}}=\sqrt{(25 + 15)(25 - 15)}\) (using the difference of squares \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{40\times10}=\sqrt{400}\).

Step3: Calculate the square root

\(\sqrt{400}=20.00\)

Answer:

\(20.00\)