Question

consider triangle def. the legs have a length of 36 units each. what is the length of the hypotenuse of the triangle? 18 units 18√2 units 36 units 36√2 units

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(DEF\) with legs \(a = 36\) and \(b = 36\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse.
Substitute \(a = 36\) and \(b = 36\) into the formula: \(c=\sqrt{36^{2}+36^{2}}\).

Step2: Simplify the expression

First, calculate \(36^{2}+36^{2}\): \(36^{2}(1 + 1)=2\times36^{2}\).
Then, \(c=\sqrt{2\times36^{2}}\).
Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 2\), \(b = 36^{2}\)), we get \(c = 36\sqrt{2}\).

Answer:

\(36\sqrt{2}\) units.