Question

An isosceles right triangle has legs of equal length. If the

hypotenuse is 10 centimeters long, find the length of each leg.

Answer 1

`\displaystyle 5√(2)`

Explanation:

we have a right angle isosceles triangle

in order to figure out the length of each leg we can consider Pythagoras theorem given by

`\displaystyle {a}^(2) + {b}^(2) = {c}^(2)`

remember that,

isosceles triangle has two equal legs so a=b and given that the the hypotenuse is 10

substitute:

`\displaystyle {a}^(2) + {a}^(2) = {10}^(2)`

simplify addition:

`\displaystyle {2a}^(2)= 100`

simplify square:

divide both sides by 2:

`\displaystyle {a}^(2)= 50`

square root both sides:

`\displaystyle {a}^{}= √(50)`

`\displaystyle {a}^{}= 5√(2)`

hence,

the length of each leg is 5√2