Question

If the angles of a triangle are 45°, 45°, and 90°,show that the length of the hypotenuse is 3 times as long as eachleg.V 1. Substitute the side lengths of the triangle into the Pythagoreantheoremq² + ² = 22. Combine like terms.

Answer 1

Acording to pythagoras theorem,

$\text{hypotenuse}^2=base^2+height^2$

Here,

$\begin{gathered} \text{hypotenuse}=c \\ \text{height}=a \\ \text{base}=a \end{gathered}$

Therefore we have,

$\begin{gathered} c^2=a^2+a^2 \\ c^2=2a^2 \\ c=\sqrt[]{2}a \end{gathered}$

Hence the proof.