Question

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

is 26 centimeters long, find the length of each leg.
hypotenuse

Answer 1

Each leg is 13√2 cm long

Explanation:

The hyotenuse of a right triangle is calculated by the formula

c² = a² + b²

where c is the hypotenuse and a, b the other sides

and then finding the square root of the above

For a right isosceles triangle the two sides a = b

So c² = a² + a² = 2a²

In the given problem the equal sides are given as x

So c² = 2x²

c = √2x

We are given c = 26

26 = √2x

x = 26/√2

Rationalizing the denominator we get

x = 26 · √2 /2

= 13√2