How to solve an unclear geometry problem — Counting line segments in a rectangle

[AgesPast]

Homework Statement

#1 I counted the line segments to divide by 120 by 8 to get 15, which is incorrect. I further exhausted my options by subtracting 48 from 120 to get 72. Then I divided 72 by 4 to get 18, but I'm still unsure if this is the correct answer.

Relevant Equations

Counting/Dividing

120-48=72
72/4=18

The solution appears too simple to be the correct to me.

 

[berkeman]

Welcome to PhysicsForums. If the area is 120 and the height is 4, what is the length of the base?

And given the length of the base, what is A?

 

[AgesPast]

If the height is 4 then the length should be 30. I am still unclear what A would be: 30/5=6. That can't be correct.

 

[Frabjous]

You have calculated that the length of the base is 30 from the function length=area/height. The length of the base can also be expressed as a function of A and 48. What is this function? You then set the two lengths equal to each other.

 

[AgesPast]

A(x)=15x-x^2

So, would this be 48=15x-x^2?

 

[Frabjous]

What is the distance between A and 48?

 

[AgesPast]

What is the distance between A and 48?

30?

 

[Frabjous]

Yes, but what is the equation for the distance between A and 48; i.e. what is formula for the distance between the two points?

 

[AgesPast]

Yes, but what is the equation for the distance between A and 48; i.e. what is the distance between the two points?

(w^2+h^2)^1/2

So, (30^2+4^2)^1/2

Correct?

 

[Frabjous]

You are thinking about this wrong.
If A = 0, what is the distance between 48 and A?
If A = 1, what is the distance between 48 and A?
Remember that A is a point, not the area.

 

[AgesPast]

Oh, this is just in terms of units right?

So, for A=0 then just 48.
A=1, then ?

 

[Frabjous]

Do you know the distance between 2 points, (a,b) and (c,d)?

 

[FactChecker]

Keep it simple. On the horizontal base-line, one end is at 48 and the length is 30, so where is the other end, where A is?

 

[AgesPast]

Do you know the distance between 2 points, (a,b) and (c,d)?

I plugged it into the distance formula (30,4) for x and (48,4) for y to get 18, but it wouldn't have occurred to me at all that I needed to go that far.

 

[Frabjous]

The distance beween 2 points is ((a-c)^2+(b-d)^2)^0.5
The left bottom quarter of the rectangle can be viewed as the point (A,0)
The right bottom quarter of the rectangle can be viewed as the point (48,0)
Plugging these in, the distance between the two bottom corners is ...

 

[AgesPast]

This is wh

The distance beween 2 points is ((a-c)^2+(b-d)^2)^0.5
The left bottom quarter of the rectangle can be viewed as the point (A,0)
The right bottom quarter of the rectangle can be viewed as the point (48,0)
Plugging these in, the distance between the two bottom corners is ...

Plugging those into the distance formula, what I got for A:

 

[Frabjous]

No, the distance is 48-A. This is the length of the base of the rectangle. Make sure that you understand how to calculate this. Set it equal to 30 and solve for A.

 

[AgesPast]

30=48-A
-18=-A
18=A

Well done, thanks.

 

[berkeman]

Whew!

 

[Mark44]

Emphasis added...

Keep it simple. On the horizontal base-line, one end is at 48 and the length is 30, so where is the other end, where A is?

The distance beween 2 points is ((a-c)^2+(b-d)^2)^0.5

As FactChecker said, keep it simple. The points in question are on a horizontal line, so to get the distance between them, just subtract the leftmost coordinate from the rightmost one. The formula above is much more general than what is required in this problem. IOW, no square roots are needed.

120-48=72
72/4=18

@AgesPast, you came up with 18 as the coordinate in post #1, but your result seems to be correct by accident. There is no logical reason you should have calculated 120 - 48 (the area minus a coordinate value), and then later divided by 4. I suspect that the answer to the problem was given, and you did some calculation unrelated to the problem to come up with that number.