The length of a leg of an isosceles right triangle is 5sqrt252. How do you find the length of the hypotenuse?

1 Answer
Jan 6, 2016

The hypotenuse
AB = 10 cmAB=10cm

Explanation:

http://mathworld.wolfram.com/IsoscelesRightTriangle.html

The above triangle is a right angled isosceles triangle , with BC = ACBC=AC

The length of the leg given =5sqrt2cm=52cm (assuming units to be in cm)

So, BC = AC = 5sqrt2 cmBC=AC=52cm

The value of the hypotenuse ABAB can be calculated using the Pythagoras theorem:

(AB)^2 = (BC)^2 +(AC)^2(AB)2=(BC)2+(AC)2

(AB)^2 = (5sqrt2)^2 +(5sqrt2)^2(AB)2=(52)2+(52)2

(AB)^2 = 50 +50(AB)2=50+50

(AB)^2 = 100(AB)2=100

(AB) = sqrt100(AB)=100

AB = 10 cmAB=10cm