Question

One leg of a 45 - 45 - 90 triangle measures 10 inches. What is the length of the hypotenuse

Answer 1

Answer:

Therefore the length of the hypotenuse is 14.14 inches.

Step-by-step explanation:

Given:

The Triangle is of 45 -45 - 90

Length of one leg = 10 inches

To Find:

Length of the hypotenuse = ?

Solution:

The Triangle is of 45 -45 - 90 ..................Given

So For 45 - 45 - 90 Both the Legs of Triangle is SAME

i.e Longer leg = Shorter leg = 10 inches

Now in Right angle Triangle By Pythagoras Theorem we have

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

On substituting the values we get

$Hypotenuse^{2}= 10^{2}+ 10^{2} \\\\Hypotenuse^{2}=200\\Square\ Rooting\ we\ get\\Hypotenuse=\sqrt{200}=10\sqrt{2}=10\times 1.414=14.14\ inches$

Therefore the length of the hypotenuse is 14.14 inches.