Find EF in the trapezoid please make sure to show your work either below
Given trapezoid ABCD with bases AD = 8 and BC = 14, and diagonal BD = 10.
We want to find segment EF.
First, we notice that triangle BCD forms a right triangle.
Using the Pythagorean theorem,
BC^2 = BD^2 + CD^2
14^2 = 10^2 + CD^2
196 = 100 + CD^2
CD^2 = 96
CD = √96 = 4√6
Since ABCD is a trapezoid, we have
AD = BC = 8, and CD = 4√6
Segment AC is the height of the trapezoid. We can find AC using the Pythagorean theorem in triangle ACD:
AC^2 = AD^2 - CD^2
AC^2 = 8^2 - (4√6)^2
AC^2 = 64 - 96
AC^2 = -32 (this is not possible, so there is an error in the given information or calculation)
We should check the given information or reassess the calculations.