Question

Need help with this one NO LINKS!!!
Special Right Triangles (Radical Answers)

Answer 1

x =
`5√(2)` (or
`(5√(2))/(1)` if it has to have a rational denominator)

Explanation:

We know;

1.) This triangle is isosceles (two of the sides are congruent).

2.) Hypotenuse is the biggest side in a right triangle. Therefore, that un-labeled side can't be 10, it has to be x as well.

So;

A² + B² = C²

x² + x² = 10²

2x² = 100

x² = 100/2

x² = 50

x =
`√(50)`

Simplifying this would result in;

`√(50)` =
`√(25) * √(2)`

`√(50)` =
`5√(2)` (or
`(5√(2))/(1)` if it has to have a rational denominator)

Hope this helps!

Answer 2

x = 5*sqrt(2)

Explanation:

Equation

Use the Pythagorean Theorem to get the value of x. If the triangle is isosceles, it means that both lets are equal to x.

x^2 + x^2 = 10^2

2x^2 = 100

x^2 = 50

x^2 = 5 * 5 * 2

sqrt(x^2) = sqrt(5*5*2)

x = 5*sqrt(2)

There is no denominator to rationalize. The answer is given as a irrational root. The only other way to present it is in an approximate decimal form.