Question

Find the value of x. Express your answer in simplest radical form

Answer 1

Since x=x, this is an isosceles right triangle.  By the Pythagorean Theorem:

h^2=a^2+b^2  (the hypotenuse squared is equal to the sum of the squared sides)

5^2=x^2+x^2

25=2x^2

2x^2=25

x^2=25/2

x=√(25/2)

x=5/√2  now if we rationalize the denominator...

x=(5√2)/(√2√2)

x=(5√2)/2