Question

if the hypotenuse of an isosceles right triangle has a length of 5 centimeters, what is the length of one of the legs? select the correct answer. 5 5√2 5√2/2

Explanation:

Step1: Apply Pythagorean theorem

Let the length of each leg be \(x\). For an isosceles right - triangle, by Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), here \(a = b=x\) and \(c = 5\). So \(x^{2}+x^{2}=5^{2}\), which simplifies to \(2x^{2}=25\).

Step2: Solve for \(x\)

Divide both sides of \(2x^{2}=25\) by \(2\): \(x^{2}=\frac{25}{2}\). Then take the square root of both sides: \(x=\sqrt{\frac{25}{2}}=\frac{5}{\sqrt{2}}\). Rationalize the denominator: \(x=\frac{5\sqrt{2}}{2}\).

Answer:

\(\frac{5\sqrt{2}}{2}\)