Solving I think an area/position type problem

[Probability]

I came across this problem today and instantly gave myself a mental block!

I was asked to fit a number plate to the front bumper of a car, the bumper from the manufacturer had two holes already drilled with captive nuts fitted for the number plate to secure to.

The number plate had no holes drilled. I looked at the front bumper and number plate and asked myself, how do I position the holes in the number plate so they line up with the bumper as vertically as possible, centralized and correctly positioned?

I could not gain access to the rear of the bumper to pencil any marks on the rear of the number plate to help position the holes to be drilled, so what good maths method is there a way to solve these types of problems?

Assume you have a rectangular plate 50 cm long and 20 cm tall with two holes drilled in it horizontally apart by 20 cm, each hole is positioned 15 cm in from the end of the rectangle, the number plate is 60 cm long and 40 cm tall. (All made up figures)

How could I use maths to accurately decide the correct position of the holes to be drilled in the number plate?

 

[stapel]

I was asked to fit a number plate to the front bumper of a car, the bumper from the manufacturer had two holes already drilled with captive nuts fitted for the number plate to secure to.

The number plate had no holes drilled....

What kind of license plate has no holes pre-drilled?!? :shock:

Before getting fancy, find out what the laws are for affixing plates to vehicles. I'll bet there are specific rules for the placement of the holes.

 

[Probability]

What kind of license plate has no holes pre-drilled?!? :shock:

Before getting fancy, find out what the laws are for affixing plates to vehicles. I'll bet there are specific rules for the placement of the holes.

Not sure which Country you are in?

UK don't supply number plates pre-drilled;-)

 

[Probability]

Apply some of Subhotosh's red ink to the bumper's captive nuts,
then push the plate against the captive nuts: you'll then get 2 red
spots on the plate...ya'll ok now

That won't work unfortunately on this occasion, the reason is that the vehicle manufacturer put the captive nuts in the bumper recessed so that the plate will sit flush to the bumper when fitted:cool:

 

[Probability]

Well then, fill the 2 bumper recesses with butter, push plate to get
2 butter spots....get it?
Wait for the butter to melt before finalizing this delicate operation.

How long should I leave the butter in the fridge so that it don't melt all down the front of the bumper:mrgreen:

Really?

I was kind of thinking there may be a formula type solution to this problem, but maybe not then?

Using made up figures this is how I see I could get round the problem.

The bumper has a rectangular section where the captive nuts are secured, the rectangular section say is a 6 x 3 cm. The captive nuts are located in the rectangle 1.5 cm down and 2 cm across.

Now say my plate is 8 cm long and 5 cm high, so drawing a template I say;

I want the bolts to be central in the number plate and fitted such that they do not make the plate illegible to read.

I measure the plate height and use the mid point of the height of the plate at 2.5 cm. I know my plate length is 8 cm and my bumper rectangle is 6 cm, so leaving 1 cm on each side I can measure 3 cm in from each side, and 2.5 cm down the plate to mark the position of the holes.

This seems like a ratio type of problem to me, but not being an expert at maths I thought maybe you guys might of been able to advise. :???:

 

[Probability]

Take the plate and draw 2 diagonals (corner to corner):
these will cross at EXACTLY the center if the plate.
Label the crossing point as C.

Draw horizontal line ACB length 2 such that AC = BC = 1.
In other words, C is center of line.
A...1...C...1...B

Yer now ready to go: A and B will hit the nuts :cool:

Thanks Denis :cool: