Answer:
[tex] \displaystyle 5\sqrt{2}[/tex]
Step-by-step 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
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
remember that,
isosceles triangle has two equal legs so a=b and given that the the hypotenuse is 10
substitute:
[tex] \displaystyle {a}^{2} + {a}^{2} = {10}^{2} [/tex]
simplify addition:
[tex] \displaystyle {2a}^{2}= 100[/tex]
simplify square:
divide both sides by 2:
[tex] \displaystyle {a}^{2}= 50[/tex]
square root both sides:
[tex] \displaystyle {a}^{}= \sqrt{50}[/tex]
[tex] \displaystyle {a}^{}= 5\sqrt{2}[/tex]
hence,
the length of each leg is 5√2
