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If the area of a rectangle is 24 and the ratio width/length = 2/3, the

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Bunuel
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If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 07:10
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If the area of a rectangle is 24 and the ratio width/length = 2/3, then the length of the rectangle is

(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
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C
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 07:17
we know that width/length = 2/3.
So, let width be 2x and length be 3x.
area = Width*length = 2x*3x = 24
6x^2=24.
Solving we get x=2.
Length = 3x = 6.
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 07:21
Suppose width=2 units and length=3 units
Thus, area= 2*3=6 sq units
however, actual area is 24 sq. units.
Thus, the scaling factor is \(\sqrt{24/6}\)=2
Thus actual length= 3*2=6
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If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 08:02
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Bunuel wrote:
If the area of a rectangle is 24 and the ratio width/length = 2/3, then the length of the rectangle is

(A) 3
(B) 4
(C) 6
(D) 8
(E) 12

\(L*W\) = rectangle area = \(24\)

\(\frac{W}{L} = \frac{2}{3}\)

\(W = \frac{2}{3}L\)

Substitute: \(\frac{2}{3}L*L = 24\)

\(\frac{2}{3}L^2 = 24\)

\(L^2 = 36\)

\(L = 6\)

Answer C
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 08:39
Bunuel wrote:
If the area of a rectangle is 24 and the ratio width/length = 2/3, then the length of the rectangle is

(A) 3
(B) 4
(C) 6
(D) 8
(E) 12


\(3x*2x = 24\)

Or, \(6x^2 = 24\)

Or, \(x^2 = 4\)

So, \(x = 2\)

Hence Length of the rectangle is 2*3 = 6

Thus, answer must be (C) 6
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 09:11
Bunuel wrote:
If the area of a rectangle is 24 and the ratio width/length = 2/3, then the length of the rectangle is

(A) 3
(B) 4
(C) 6
(D) 8
(E) 12



since the ratios are given,,,, let the sides be 2x and 3x...

area = 2x * 3x = 6x^2 = 24

solving the above equation we can get the value of x = 2...

length = 6
anc C
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 22:20
Bunuel wrote:
If the area of a rectangle is 24 and the ratio width/length = 2/3, then the length of the rectangle is

(A) 3
(B) 4
(C) 6
(D) 8
(E) 12


Let width and length of rectangle be 2x and 3x
Area = 24
=> 2x * 3x = 24
=> x^2 = 4
=> x = 2

Length = 3x = 6

Answer C
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If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   01 Oct 2017, 23:23
Bunuel wrote:
If the area of a rectangle is 24 and the ratio width/length = 2/3, then the length of the rectangle is

(A) 3
(B) 4
(C) 6
(D) 8
(E) 12



\(\frac{Width}{Lenght} =\frac{2}{3} =\frac{4}{6}=\frac{8}{12}\)

Only \(\frac{4}{6}\) gives required area 24

\(Lenght=6\)

Answer: C
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   04 Oct 2017, 16:39
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Bunuel wrote:
If the area of a rectangle is 24 and the ratio width/length = 2/3, then the length of the rectangle is

(A) 3
(B) 4
(C) 6
(D) 8
(E) 12


We can express the ratio of width to length as 2x : 3x. We can create the equation for the area as:

(2x)(3x) = 24

6x^2 = 24

x^2 = 4

x = 2

Thus, the length of the rectangle is 3(2) = 6.

Answer: C
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink] New post   14 Oct 2017, 10:36
we know that width/length = 2/3.
So, let width be 2x and length be 3x.
area = Width*length = 2x*3x = 24
6x^2=24.
Solving we get x=2.
Length = 3x = 6.
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the [#permalink]
14 Oct 2017, 10:36
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