Question 49768: I am actually baffled, I am asking this for my daughter, I cannot help her because my math is very limited so even if I read how to solve I would not get very far. It is a story problem involving geometry (I think). Here is her story problem question:
To promote a new delivery service, Pizzaroo is including a free 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 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.
Thanks for your help in advance!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I am actually baffled, I am asking this for my daughter, I cannot help her because my math is very limited so even if I read how to solve I would not get very far. It is a story problem involving geometry (I think). Here is her story problem question:
To promote a new delivery service, Pizzaroo is including a free 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 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.
Thanks for your help in advance!
GOOD PROBLEM.TRY TO TO DRAW A FIGURE AS DESCRIBED BELOW FOR BETTER UNDERSTANDING
LET THE CENTRE OF CIRCULAR PIZZA BE 'C'.THIS IS SAME AS THE CENTRE OF THE BOX.LET THE CARD BE PQRS..LET IT TOUCH THE CIRCULAR PIZZA AT P.JOIN OP
OP IS THE RADIUS=R SAY TO BE FOUND.WE HAVE..
PQ=RS=140....
PS=QR=70...GIVEN
DRAW CT FROM CENTRE C A RADIUS PERPENDICULAR TO RS.
EXTEND QP TO MEET CT AT X.
WE HAVE CT=RADIUS=R=CP
PSTX IS A RECTANGLE.
PS=70=XT
PX=QPX-QP=R-140
CX=CXT-XT=R-70.
NOW IN THE RIGHT ANGLED TRIANGLE CPX,WE HAVE
CP=R=HYPOTENUSE
CX=ONE SIDE=R-70
PX=ANOTHER SIDE=R-140
USING PYTHOGARUS THEOREM ,WE HAVE....HYPOTENUSE^2=SIDE^2+SIDE^2
R^2=(R-70)^2+(R-140)^2
R^2=R^2-140R+4900+R^2-280R+19600
R^2-420R+24500=0
R^2-70R-350R+24500=0
R(R-70)-350(R-70)=0
(R-70)(R-350)=0
R-70=0.....OR....R=70....NOT POSSIBLE AS THEN IT TOUCHES THE LOWER EDGE OVERLAPPING THE PIZZA.
R-350=0......R=350 IS THE ANSWER.
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