# Easy? trig?

1. Aug 28, 2006

### 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

2. Aug 28, 2006

### 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

3. Aug 28, 2006

### Office_Shredder

Staff Emeritus
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?

4. Aug 29, 2006

### 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.

5. Aug 29, 2006

### VietDao29

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

6. Aug 29, 2006

### 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.

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7. Aug 29, 2006

### 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? :)

Last edited: Aug 29, 2006
8. Aug 31, 2006

### kappcity06

Last edited: Aug 31, 2006
9. Aug 31, 2006

### Integral

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

10. Aug 31, 2006

### kappcity06

11. Sep 2, 2006

### VietDao29

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

12. Sep 2, 2006

### Integral

Staff Emeritus
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