How would you solve for X if X was the hypotenuse of a 45-45-90 triangle and the other two sides were Square Root of 11?
Use Pythagoras theorem:
hypotenuse² = side1²+side2²l
=(√11)²+(√11)²
= 11 + 11
= 22
Therefore
hypotenuse = √22
Thank you very much! I thought it was 2 Square Roots of 11. You saved me.
The method I have shown above is more general, and applies to any right-triangle.
For a 45-45-90 triangle, you were close with the answer. A short-cut would be to multiply each side by √2, which makes:
√2 * √11
=√22.
To solve for X, the hypotenuse of a 45-45-90 triangle, you can use the relationship between the sides of such a triangle. In a 45-45-90 triangle, the two legs are congruent, meaning they have the same length.
In this case, you are given that both legs of the triangle have a length of the square root of 11. So, let's label one of the legs as 'a' and the hypotenuse as 'x'. The other leg will also be 'a' due to the congruency.
According to the relationship in a 45-45-90 triangle, the length of the hypotenuse (x) is equal to the square root of 2 times the length of either of the legs (a). Mathematically, it can be written as:
x = √2 * a
Substituting the value of 'a', which is the square root of 11:
x = √2 * √11
x = √(2 * 11)
x = √22
Therefore, the length of the hypotenuse (X) is the square root of 22 (√22).