Answer:
x = 13
Explanation:
The diagonals of rhombi are perpendicular and form a right angle at their intersection. Furthermore, they bisect each other and create four congruent segment. Thus, the measures of the other two sides of the triangle shared by x is 5 and 12.
Thus, x is the hypotenuse of the triangle and is opposite the right angle.
Since we have a right triangle, we can find x using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
- a and b are the shorter sides called legs,
- and c is the longest side of the hypotenuse.
We plug in 5 and 12 for a and b, allowing us to solve for c (aka x):
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
13 = c
Thus, x = 13 units