Mystery of the Perfectly-Circular Pizza: What's the Diameter?

[kappcity06]

a perfectly-circular pizza comes in a square box with a card in the box. the card measures 140mm by 70 mm. what is the diameter of the pizza?

i tried similar squares but this did not work? any help anyone

 

[kappcity06]

i set it up trying to solve for 2 equation but that didn't work either. i got

A=39200+140y+280x+xy
P=156800+560y+1120x+4xy

i do not know how to attempt to solve these

 

[Office_Shredder]

Is that the full question? I don't understand how the card is oriented... I assume it's next to the pizza, but are the sides parallel to the box's, or is it angled to fit best?

 

[kappcity06]

the card is at the corner of the pizza box barely touching the pizza.

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that is where the card is. (sorry for the pic) the longer side is out. imagine the pizza being in that square.

 

[VietDao29]

i set it up trying to solve for 2 equation but that didn't work either. i got

A=39200+140y+280x+xy
P=156800+560y+1120x+4xy

i do not know how to attempt to solve these

Where did you get 39200, and 156800? I cannot see that information anywhere from the problem you posted...

 

[kappcity06]

for A=39200+140y+280x+xy i did Area=(140+x)(280+y). and for P=156800+560y+1120x+4xy i did perimiter=(280+2x)(560+2y). so is wrong though. it should be perimiter=(280+2x)+(560+2y). see the attached picture. the x is on the right and left and the y is top and bottom.

 

[VietDao29]

No, you don't need to use area in this problem. Here's how I'd approach the problem:

In the picture, the card is green, the pizza is red, the light green line segment has the length of a, the purple line segment has the length of b. The two light blue line segments have the same length, sice they are the diagonals of a rectangle.
So we have:
a + 140 = b + 70 = R (where R is the radius of the pizza)
<=> a = b - 70. Right?
We also have:
a² + b² = R² = (a + 140)².
Do you know why?
So we need to solve for a, and b (i.e 2 unknowns), and we have 2 equations:
$$\left\{ \begin{array}{clc} a & = & b - 70 \\ a ^ 2 + b ^ 2 & = & (a + 140) ^ 2 \end{array} \right.$$
Is there anything unclear from my post that you don't understand? :)
Can you go from here? :)

 

[kappcity06]

is the answer 700

 

[Integral]

You are not there yet. What is the quantity you solved for? Where is it on the drawing? How does it relate to the radius of the pizza?

 

[kappcity06]

no that is the answer

 

[VietDao29]

is the answer 700

Yes , but to be more exact, it is 700 mm.

 

[Integral]

I think I posted that while the op was editing. I responed to a post that gave the vaule of b as the answer. 700mm is correct