gwenspooner85

Notice that we have two similar triangles here. The first one has sides 20 and 24. The second has sides 20+30=50 and 24+x. Since they are similar the ratios of the corresponding sides must be the sae.

We have:

20/50=24/24+x

480+20x=1200

20x=720

x=36

Hi, I don't know you but welcome back! :)

We write the slope intercept form equation first based on the two given points. The slope is -4/9. We now have y=-4/9x+b. We then plug in one of the points to determine b. 

y=-4/9x+b

-2=-4/9(4)+b

-2=16/9+b

b=-2/9

So the equation is y=-4/9x-2/9. We then convert it to standard form.

y=-4/9x-2/9

4/9x+y=-2/9

4x+9y=-2

AoPS copyright claim

The lateral surface area is 4(1/2*24*32).

4(1/2*24*32)

=4(12*32)

=1536

Notice that CD=US, UT=CB, and BD=ST. In other words, the two triangles are congruent.

Since CD=US:

3x+32=9x-4

6x=36

x=6

Since BD=ST:

y=2y-20

y=20

Keep in mind squars are also rectangles. There are 7 squares.

rectangles composed of 2 squares: 8

rectangles composed of 3 squares: 2

rectangles composed of 4 squares(forms a larger square): 2

So in total I believe there are 7+8+2+2=15+4=19 rectangles.