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: Identify triangle type

Triangle DEF is a right - isosceles triangle (two legs equal, right angle at F), so we can use the Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\), where \(a = b=36\) (the legs) and \(c\) is the hypotenuse.

Step2: Apply Pythagorean theorem

Substitute \(a = 36\) and \(b = 36\) into the formula:
\(c=\sqrt{36^{2}+36^{2}}=\sqrt{2\times36^{2}}\)
We know that \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), so \(\sqrt{2\times36^{2}}=\sqrt{2}\times\sqrt{36^{2}}\)
Since \(\sqrt{36^{2}} = 36\) (because \(\sqrt{x^{2}}=\vert x\vert\) and \(x = 36>0\)), then \(c = 36\sqrt{2}\)

Answer:

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