For all positive values of P, W, L, and A, consider the family of rect

Question

For all positive values of P, W, L, and A, consider the family of rectangles having perimeter P feet, width W feet, length L feet, and area A square feet.

In the first column of the table, select the expression in terms of P and W that is equivalent to A, and in the second column of the table select the expression in terms of P and W that is equivalent to L. Select only two expressions, one in each column.

Sajjad1994 · Accepted Answer

Official Explanation

For all positive values of P, W, L, and A, consider the family of rectangles having perimeter P feet, width W feet, length L feet, and area A square feet.
 
In the first column of the table, select the expression in terms of P and W that is equivalent to A, and in the second column of the table select the expression in terms of P and W that is equivalent to L. Select only two expressions, one in each column.

Strategize

For any rectangle, A = LW, and P = 2L + 2W. Dividing both sides of the latter equation by 2 yields P/2 = L + W, and subtracting W from both sides yields     = L. Therefore L =     and
A = LW

=  (\frac{P}{2} -W)W

Alternatively, observe that, since A = LW, the expression for A is equivalent to the expression for L with an additional factor, W. And the only two expressions in the list that have this relationship are C,  (\frac{P}{2}-W) , and E,  (\frac{P}{2} -W)W

RO1, A: Strategize

The correct answer is E,  (\frac{P}{2} -W)W

RO2, L: Strategize

The correct answer is C,  (\frac{P}{2} -W)

jhavyom · Answer

For all positive values of P, W, L, and A, consider the family of rectangles having perimeter P feet, width W feet, length L feet, and area A square feet. In the first column of the table, select the expression in terms of P and W that is equivalent to A, and in the second column of the table select the expression in terms of P and W that is equivalent to L. Select only two expressions, one in each column.

For length L, and width W.
Area, A = LW
Perimeter, P = 2L + 2W
So, P/2 = L + W...(i)
Rearranging (i)
L = P/2 - W

Now A = LW = (P/2-W)W

For length L, and width W.
Area, A = LW
Perimeter, P = 2L + 2W
So, P/2 = L + W...(i)
Rearranging (i)
 L = P/2 - W

Now A = LW =  (P/2-W)W

Sumi1010 · Answer

For the rectangle :

Area A = width W x length L i.e.
  A=WL  --- 1
Perimeter P = 2 x (width W + length L) i.e. 
 P= 2(W+L)  --- 2

From 1 and 2, 
 L  =  A/W =  (P/2) - W  
Thus A =   W

Hence, 
L = (P/2) - W
A =   W

rocky620 · Answer

For a Rectangle
Area=Length*Width
A=L*W....... Eq1

Perimeter=2(Length+Width)
P=2(L+W)
 \frac{P}{2} =L+W
 \frac{P}{2}  - W = L......... Eq2

Putting Value of L from Eq2 in Eq1

A= \frac{P}{2}  - W]*W

A=( \frac{P}{2}  - W)W ; L= \frac{P}{2}  - W

Deepakjhamb · Answer

we need A = F( P,W) and L =F (P,W)

So we have A =L*W -EQ -1 
 P= 2(L+W) - EQ 2

SO L= P/2 - W

SO A = (P/2-W) *W

are the answers

TarunKumar1234 · Answer

Given, P= 2(W+L) and A = W*L
So,  A= (P/2 * -W) *W

Further,  L  = A/W = (P/2 * -W) *W/W =  (P/2 * -W)

Tanpok · Answer

Bunuel  will this show up on Gmat Focus??

Bunuel · Answer

I think, it still can be tested.

Check these two topics:

GMAT Syllabus for Focus Edition  
  Geometry Tested on GMAT Focus?

While specific geometry knowledge is not tested on GMAT Focus, not everything involving shapes, volumes, or areas requires specialized geometry knowledge. The area of a square or rectangle, the volume of a cube or rectangular solid, and  the Pythagorean theorem  are not considered specific geometry knowledge by the GMAT and can still be tested. Moreover, a question can involve shapes but test another area, such as combinations or other topics. There are several  questions involving these concepts in the GMAT Prep Focus mocks .

The chapter on coordinate geometry, including planes and slopes, is still present in the recent Official Guides. That said, it is tested to a much smaller extent. For example, you might see some questions involving graphs, either in Problem Solving or in Data Insights graph-based questions. However, those usually fall under the functions category rather than pure coordinate geometry, so they typically won’t involve distance calculations, angles, or similar topics.

A	L	Expression
		\(\frac{P^2}{W}\)
		\(\frac{PW}{4}\)
		(\(\frac{P}{2}-W\))
		\(\frac{(P-W)^2}{4}\)
		\((\frac{P}{2}-W)W\)

For all positive values of P, W, L, and A, consider the family of rect

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For all positive values of P, W, L, and A, consider the family of rect

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