Answer:
x = 5*sqrt(2)
Step-by-step 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.
Answer:
x = [tex]5\sqrt{2}[/tex] (or [tex]\frac{5\sqrt{2}}{1}[/tex] if it has to have a rational denominator)
Step-by-step 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 = [tex]\sqrt{50}[/tex]
Simplifying this would result in;
[tex]\sqrt{50}[/tex] = [tex]\sqrt{25} * \sqrt{2}[/tex]
[tex]\sqrt{50}[/tex] = [tex]5\sqrt{2}[/tex] (or [tex]\frac{5\sqrt{2}}{1}[/tex] if it has to have a rational denominator)
Hope this helps!