Answer:
d = 19
Explanation:
First, you need to find the length of the diagonal of the rectangular base of the prism. It's the dashed segment on the base of the prism.
The base of the prism is a rectangle with sides 10 and 6. We can use the Pythagorean theorem to find the diagonal.
10^2 + 6^2 = x^2
100 + 36 = x^2
x^2 = 136
x = sqrt(136)
The dashed diagonal of the rectangular base has length sqrt(136).
Now you use the dashed diagonal and the vertical side measuring 15 as the legs of another right triangle. The diagonal labeled d is the hypotenuse of this triangle. We use the Pythagorean theorem again.
15^2 + (sqrt(136))^2 = d^2
225 + 136 = d^2
d^2 = 361
d = 19