Answer:
AC=8.2m
AD=8.6m
Explanation:
Because this is a rectangular prism, all of the angles are right angles. Thus, we can use the pythagorean theorem on the triangles formed to solve for the missing side lengths.
First, we need to solve for AC in order to solve for AD. ACB is a right triangle, so we can use the pythagorean theorem.
AB^2+BC^2=AC^2.
Substituting, we get
6.5^2+5.0^2=AC^2
67.25=AC^2
Taking the square root of both sides, we get
8.2≈AC
Next, we can use the pythagorean theorem on right triangle ADC again.
AC^2+DC^2=AD^2
Substituting, we get
8.2^2+2.5^2=AD^2
73.49=AD^2
Taking the square root of both sides gives us
8.6≈AD
Side note: the symbol ≈ means approximately. In this case, I rounded the numbers to the nearest tenth, because that's what the question wants.