Answer:
Each of the legs of isosceles right triangle is 5
Step-by-step explanation:
Watch the attached figure for the isosceles right angled triangle
Looking at the figure we see that AB=5√6 and BC=CA
According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.
1) Applying the Pythagorean theorem to the isosceles right triangle, we have
2) Let BC=a and CA=a as they both are equal
So,
=>
=>
=> (since √6*√6 = (√6)²= 6)
=>
3) Dividing both sides by 2, we get
4) Cancelling out the 2's on the left, we get
= 75
5) Taking the square root on both sides, we have
=> a = 5
So,
Each of the legs of isosceles right triangle is 5
