Question

an isosceles right triangle has two identical legs with lengths of 9 millimeters. if the length of the triangles hypotenuse, in millimeters, can be written in the form ( xsqrt{2} ), where ( x ) is an integer, what is the value of ( x )?
a 3
b 6
c 9
d 81

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 9\) and \(b = 9\) (since it's an isosceles right - triangle), and hypotenuse \(c\), by the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\).
Substitute \(a = 9\) and \(b = 9\) into the formula: \(c^{2}=9^{2}+9^{2}\).

$$
LATEXBLOCK0
$$

Step2: Compare with the given form \(x\sqrt{2}\)

We are given that \(c=x\sqrt{2}\). Since \(c = 9\sqrt{2}\), by comparing the two expressions \(x\sqrt{2}\) and \(9\sqrt{2}\), we can see that \(x = 9\).

Answer:

C. 9