NeoPets Riddles (Lenny Conundrums) and Answers Here

To promote a new delivery service, Pizzaroo is including a free Neopets Collectable Card with every pizza purchase. What a deal! So you decided to order a Jelly Bean Pizza. Yum!


When the pizza arrived, you noticed that the free Neopets Collectable Card was in the corner of the square box, so that its corner just barely touched the outside of the perfectly-circular pizza. The Collectable Card measures exactly 140 mm by 70 mm.


What is the diameter of the pizza, in millimetres? Please round to the nearest millimetre.




P.S. Unfortunately, because of the difficulty in delivering a jelly bean pizza without all of the jelly beans falling off, the pizza delivery service was discontinued soon after it began.


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*rubs hands together*
I can figure this one out!
I'm sure.

New Lenny!
To promote a new delivery service, Pizzaroo is including a free Neopets Collectable Card with every pizza purchase. What a deal! So you decided to order a Jelly Bean Pizza. Yum!

When the pizza arrived, you noticed that the free Neopets Collectable Card was in the corner of the square box, so that its corner just barely touched the outside of the perfectly-circular pizza. The Collectable Card measures exactly 140 mm by 70 mm.



What is the diameter of the pizza, in millimetres? Please round to the nearest millimetre.

lenny
5 cards would go across the exact center of the pizza giving a total of 700. now im not sure what other figure to multiply by to get the diameter. i hate algebra problems

set up a coordinate system, witht he center of the circle as the origin. apply the characteristic cirlce equation with center at (0,0)

x^2+y^2 = 0,. With the cirlcue info the corner of the card is on the cirlce so we use the card's dimensions and obtain:

(r-140)^2+(r-70)^2=r^2 , where r is the RADIUS of the circle. solve the quadratic. I dont' post answers, just solutions.

Draw X & Y axes through the circle.
Draw a line from origin to the point where the card touches.
Drop a vertical line from that point, forming a right triangle.

Call the x portion of the axis which makes the base of triangle "x"
Call the vertical you dropped "y"

X^2 + y^2 = R^2
R = X + 140
R = y + 70

X = R - 140
Y = R - 70

Substitute:
(R-140)^2 + (R-70)^2 = R^2

Multiply out:
R^2 - 280R + 19600 + R^2 - 140R + 4900 = R^2

Simplify:
R^2 - 420R + 24500 = 0

Solve the quadratic:

R = -(-420) +/- sqrt((-420)^2 - (4 * 1 * 24500))
----------------------------------------------------
2 * 1

The whole thing divided by 2 or just the right side of the =?

rrr

I should be able to do this no problem, why am I having such a hard time?

Ugh..it must be because of summer break.

I keep getting a negative..

Simplifying
r2 + -280r + 19600 + r2 + -140r + 4900 = r2

Reorder the terms:
19600 + 4900 + -280r + -140r + r2 + r2 = r2

Combine like terms: 19600 + 4900 = 24500
24500 + -280r + -140r + r2 + r2 = r2

Combine like terms: -280r + -140r = -420r
24500 + -420r + r2 + r2 = r2

Combine like terms: r2 + r2 = 2r2
24500 + -420r + 2r2 = r2

Solving
24500 + -420r + 2r2 = r2

Solving for variable 'r'.

Combine like terms: 2r2 + -1r2 = 1r2
24500 + -420r + 1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
24500 + -420r + 1r2 = 0

Factor a trinomial.
(70 + -1r)(350 + -1r) = 0

Subproblem 1Set the factor '(70 + -1r)' equal to zero and attempt to solve:

Simplifying
70 + -1r = 0

Solving
70 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-70' to each side of the equation.
70 + -70 + -1r = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -1r = 0 + -70
-1r = 0 + -70

Combine like terms: 0 + -70 = -70
-1r = -70

Divide each side by '-1'.
r = 70

Simplifying
r = 70
Subproblem 2Set the factor '(350 + -1r)' equal to zero and attempt to solve:

Simplifying
350 + -1r = 0

Solving
350 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-350' to each side of the equation.
350 + -350 + -1r = 0 + -350

Combine like terms: 350 + -350 = 0
0 + -1r = 0 + -350
-1r = 0 + -350

Combine like terms: 0 + -350 = -350
-1r = -350

Divide each side by '-1'.
r = 350

Simplifying
r = 350

Solution r = {70, 350}

Because we know that the card has a dimention of 70 then the radius has to be 350

And diameter is 2R.

So it is 700?

~.~

lenny
i understand the work you posted but are you not just finding the radius of the problem and not the diameter that is twice the size of the radius

I'm aware of that, that is why i didn't put 350 as my answer

The card's length is 140mm and it will fit across 5 times. 140 x 5 = 700

Seems too easy, but wouldn't that be the diameter?

If you think about it, the answer is 700mm because 5 cards across=700mm and the pizza goes from one side of the box to the other and its a circle so it soednt matter where the center line is.

I got 2408mm

diameter=700
radius=350
2*3.14*r
6.28*350

2408mm

sorry homez it cant be that high remember were only looking for the diameter so stick to your 700

o nd by the way i did the quadratic formula...but the problem is just like most quadratics... theres 2 answers to it....490 & -70

Hello,

I am a little confused as to what the answer might be. Can someone please tell me is the answer -70 or is the answer 700? I'd appreciate whatever help you have to offer. Thank You!

Oh woops that area

The answer can't be -70 candi.