Question

the hypotenuse of an isosceles right triangle is 6 centimeters long. how long are its sides? (round your answer to two decimal places.) cm

Explanation:

Step1: Apply Pythagorean theorem

Let the length of each of the equal sides be \(x\). For a right - triangle, \(a^{2}+b^{2}=c^{2}\). In an isosceles right - triangle \(a = b=x\) and \(c = 6\). So, \(x^{2}+x^{2}=6^{2}\).

Step2: Simplify the equation

\(2x^{2}=36\). Then \(x^{2}=\frac{36}{2}=18\).

Step3: Solve for \(x\)

\(x=\sqrt{18}\). Since \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\approx3\times1.414 = 4.24\)

Answer:

\(4.24\)