Question

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

Explanation:

Step1: Identify triangle type

Triangle DEF is a right - isosceles triangle (right angle at F, two angles 45°), so legs \(a = b=36\) units.

Step2: Apply Pythagorean theorem

For a right triangle, hypotenuse \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 36\), \(b = 36\):
\(c=\sqrt{36^{2}+36^{2}}=\sqrt{2\times36^{2}} = 36\sqrt{2}\) units.

Answer:

\(36\sqrt{2}\) units (corresponding to the option "36√2 units")