A pie can be cut into seven pieces with three straight cuts. What is the largest number of pieces that can be made with eight straight cuts?
A. 29
B. 33
C. 37
D. 41

You have to think in three dimensions to answer this properly. The relative size of the pieces was never specified, so let’s start with the first three cuts:

Cut 1: No specified angle—-but it’s vertical and along a diameter (assuming a circular pie): 2 pieces.

Cut 2: Perpendicular to Cut 1; also vertical: 4 pieces.

Cut 3: Horizontal across the midline of the pie: 8 pieces.

Cuts 4 and 5: Diagonally—from either end of cut 1 on top to the opposite sides on the bottom (they intersect at the center): 16 pieces.

Cuts 6 and 7: Diagonally from the ends of cut 2 (similar to cuts 4 and 5): 32 pieces.

Cut 8: The exact angle is unimportant—it’s difficult if not impossible to cut more than half of the pieces. So of 32, 16 are split, leaving a grand total of 48 pieces.

There could very well be a way to make more than 48 pieces, but I would have written that one if I’d thought of it.

Step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3