you decide to build a trapezoidal prism birdhouse for a summer project the dimension for The birdhouse are as follows front and back. what are the dimensions of the top and bottom rectangle?​

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute:

the answer is 9 because the question is telling how much it be together.