QZ wrote:
A rectangular sandbox has a width of W feet, a perimeter of P feet, and an area of A square feet. Which of the following equations must be true?
a. \(W^2 + PW + A = 0\)
b \(W^2 - PW + A = 0\)
c. \(2W^2 + PW + 2A = 0\)
d. \(2W^2 - PW - 2A = 0\)
5. \(2W^2 - PW + 2A = 0\)
PKN wrote:
PKN wrote:
generis wrote:
From perimeter equation, find L in terms of W*
\(P = 2L + 2W=2(L+W)\)
\(\frac{P}{2}=L + W\)
\(L=\frac{P}{2}-W\)
Set up the equation for area, substitute for \(L\) from above
\(A=(W*L)\)
\(A=W*(\frac{P}{2}-W)\)
\(\frac{PW}{2}
- W^2=A\)
\(PW -2W^2=2A\)
Move LHS terms to RHS. Signs change
\(2W^2 - PW + 2A = 0\)
Answer E
*There is no L in the equation, but W, P, and A ARE in the equation. Both P and A involve both W and L. Thus L must be defined in terms of \(W\)
Hi
generis pushpitkc ,
Could you please explain the logic behind highlighted texts?
Thanking you.
Thank you
pushpitkcI have two points :-
1. Can we assume in
"must be true question" ?
2. How can a rectangular box(=cuboid) be assumed as a rectangle, I mean a 3D figure to a 2D figure though it is known that the faces of the rectangular sand box
are rectangular surfaces.
Or, Is it a trap that we have to assume the given box as a rectangle
since perimeter is given and perimeter is calculated for only 2-D surfaces.
I think the question may be missing something or I may be missing concepts.
Pardon me for any trouble.
Thanking you
PKN , questions are not trouble.
Quote:
1. Can we assume in "must be true question" ?"
I'm not sure quite what you mean by this question.
Can we assume... What? This question does not provide three options, for example, from which we must choose one, two, three, all, or none.
Must be true seems to mean "only one of these equations is correct." As far as I can tell, "must be" means "is."
Quote:
Or, Is it a trap that we have to assume the given box as a rectangle since perimeter is given and perimeter is calculated for only 2-D surfaces.
I think the word "box" in "sandbox" might be a trap if we overthink.
I do not think the question is flawed, and I do not think you are missing concepts. In fact, I think you grasped the logic quite well.
Either we ignore volume because we see it is not included, or we consider that we are dealing with a 3-D figure, but we are being asked 2-D questions.
We do not have enough typical information for a 3-D figure. Not one of the terms in any of the equations is cubed -- that is, volume is not at issue.
The emphasis is on rectangle -- perimeter and area.
If the given information's limits do not stop doubt about a 3-D prism, assume that the question asks about one face: the top of the sandbox.
In plane geometry:
-- P, perimeter is a linear measurement
-- A, area is measured in square units
-- V, Volume is measured in cubic units
We have L and W in linear feet
We do not have height, H
We have area, A, in square feet
There is no mention of cubic feet
Further, we have a
rectangle.
A cube with equal W, L, and H would give us a third measurement that a rectangle cannot.
From those facts, I think we can infer that we are being asked about the sandbox as if it were a fenced-in piece of grass, for example.
Alternatively, we can infer from what is given that we are being asked about only one of the surface areas of the sandbox.
We can ask two dimensional questions about three dimensional figures.
As mentioned, this question asks about the top "face" of the sandbox.
I worked backwards from what we were given.
L and W will yield Perimeter
L and W will yield Area
L does not appear in the answers.
W\(^2\) appears in all the answers.
Area requires square units. W\(^2\) will provide square units.
Hence: use perimeter and width to redefine length in terms of W and P. The latter appear in all of the equations.
Use area to get a squared term.
Essentially, do we we understand the relationship among width, length, perimeter, and area?
Do we see that we must:
-- redefine length in terms of W and P
-- use the relationship between A and P, and
-- form an equation?
That's it.
I hope that helps.
**Some people in specialized areas calculate what they call the perimeter of a 3-D figure. That usually means the total length of the edges. I'm not a specialist in those areas. Nor do I think GMAT expects any of us to be such specialists. _________________
People wish to learn to swim and at the same time to keep one foot on the ground. -- Marcel Proust