Question

Consider triangle DEF. The legs have a length of 36 units

What is the length of the hypotenuse of the triangle

18 units

1872 units

36 units

36/7 units

Answer 1

`\large \boxed{36√(2)\text{ units}}`

Explanation:

Assume ∆DEF looks like the one below.

We can use Pythagoras' Theorem to find the hypotenuse f.

`\begin{array}{rcl}d^(2) + e^(2) & = & f^(2)\\36^(2) + 36^(2) & = & f^(2)\\f^(2) & = & 2 * 36^(2)\\f & = & \sqrt{2 * 36^(2)}\\& = & 36√(2)\\\end{array}\\\text{The length of the hypotenuse is $\large \boxed{\mathbf{36√(2)}\textbf{ units}}$}`