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

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

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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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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the  [#permalink]

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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]

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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]

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01 Oct 2017, 08:02
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: $$\frac{2}{3}L*L = 24$$

$$\frac{2}{3}L^2 = 24$$

$$L^2 = 36$$

$$L = 6$$

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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the  [#permalink]

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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]

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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
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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the  [#permalink]

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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

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

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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

$$Lenght=6$$

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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the  [#permalink]

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04 Oct 2017, 16:39
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

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.

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Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the  [#permalink]

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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.
Re: If the area of a rectangle is 24 and the ratio width/length = 2/3, the &nbs [#permalink] 14 Oct 2017, 10:36
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# If the area of a rectangle is 24 and the ratio width/length = 2/3, the

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