I need help with this math problem? You had a pizza delivered and in the pizza box there was a scratch card in

Question

I need help with this math problem? You had a pizza delivered and in the pizza box there was a scratch card in the corner just barely touching the outside of the perfectly circular pizza. The scratch card measured exactly 140mm by 70mm. What is the diameter of the pizza in millimetres and round to the nearest millimetre. And if possible can you show me how you got the answer because I have another problem just like that one.

Answer 1

In order to solve this problem, we assume that the pizza just barely fits inside the pizza box. This means that the distance from the center of the pizza box to any side is equal to the radius of the pizza. If we superimpose a cartesian coordinate system on the box with the origin at the center, this means that the sides of the box correspond to the lines x=r, y=r, x=-r, and y=-r (well, actually segments of those lines, since the sides of the box are not infinitely long). We may assume without loss of generality that the scratch card is in the upper-right hand corner of the box. This means that the upper-right hand corner of the scratch card is at (r, r), and therefore the lower-left hand part of the card is at (r-w, r-l) where w and l are the width and length of the card, respectively. We can also assume without loss of generality that the the measurement of 140 corresponds to the width of the card, thus the location of this point is (r-140, r-70). We also know that this point is on the outside of the pizza, thus it must lie at a distance r from the origin, where r is the radius of the pizza. This means that we can write the following system of equations describing the point's location:

x=r-140
y=r-70
x²+y²=r² (by the pythagorean theorem)

We now merely have to solve this system of equations for r. Substitute the first two equations into the third and we get:
(r-140)²+(r-70)²=r²
Expand these terms:
r²-280r+19600+r²-140r+4900=r²
Simplify:
r²-420r+24500=0
Complete the square:
r²-420r+44100=19600
Simplify:
(r-210)²=19600
Take the square root:
r-210=±140
Solve:
r=210±140
r=350 or r=70

Note that there are two possible solutions. Both of these solutions describe a point where the card's lower-left corner just barely touches the pizza, but in the r=70 case, the card covers half the pizza and touches the point on the opposite side - clearly not what we want. Thus the correct solution is a radius of 350 mm, which gives us a diameter of 700 mm, or about 27.5 inches. That's a big pizza!

Answer 2

Do you go through this every time you receive a Pizza with a scratch card included in the box. If I were you I would tell Pizza Hut or whoever you order Pizza from to not include a scratch card with your order.

Answer 3

It seems to me that there is some information missing from this question....like how big is the pizza box?

Answer 4

Pascal is right. In general, if the card has dimension a x b, then the diameter r is

r = a+b+sqrt(2ab) or r = a+b-sqrt(2ab)

Answer 5

eat the pizza.

Answer 6

1570 mm.
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