## The rectangle A has a (width) and b (height) and another...

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### The rectangle A has a (width) and b (height) and another...

by AAPL » Thu Mar 15, 2018 4:56 am
The rectangle A has a (width) and b (height) and another rectangle B has c (width) and d (height). If a/c = b/d = 3/2, what is the ratio of the rectangle A's area to the rectangle B's?

A. 3/2
B. 3/4
C. 9/2
D. 9/4
E. 27/8

The OA is D.

Can I say that,

a = 3k, c = 2k, b = 3m and d = 2m, since a, b and c, d are multiples of 3 and 2 respectively.

Then the ratio of the area will be,
$$\frac{3k}{2k}:\frac{3m}{2m}=9km:4km=\frac{9}{4}$$
Is there another strategic approach to solve this PS question? Can any experts help, please? Thanks!

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by [email protected] » Thu Mar 15, 2018 5:29 am
AAPL wrote:The rectangle A has a (width) and b (height) and another rectangle B has c (width) and d (height). If a/c = b/d = 3/2, what is the ratio of the rectangle A's area to the rectangle B's?

A. 3/2
B. 3/4
C. 9/2
D. 9/4
E. 27/8

The OA is D.

Can I say that,

a = 3k, c = 2k, b = 3m and d = 2m, since a, b and c, d are multiples of 3 and 2 respectively.

Then the ratio of the area will be,
$$\frac{3k}{2k}:\frac{3m}{2m}=9km:4km=\frac{9}{4}$$
Is there another strategic approach to solve this PS question? Can any experts help, please? Thanks!
You could also just pick numbers.
If a/c = 3/2, say a = 3 and c = 2
If b/d = 3/2, say b = 3 and d = 2

If the first rectangle has sides of a and b, or 3 and 3, it will have an area = 3*3 = 9
If the second rectangle has sides of b and d, or 2 and 2, it will have an area = 2*2 = 4.
The ratio = 9/4. The answer is D
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by [email protected] » Thu Mar 15, 2018 5:55 am
AAPL wrote:The rectangle A has a (width) and b (height) and another rectangle B has c (width) and d (height). If a/c = b/d = 3/2, what is the ratio of the rectangle A's area to the rectangle B's?

A. 3/2
B. 3/4
C. 9/2
D. 9/4
E. 27/8

The OA is D.

Can I say that,

a = 3k, c = 2k, b = 3m and d = 2m, since a, b and c, d are multiples of 3 and 2 respectively.

Then the ratio of the area will be,
$$\frac{3k}{2k}:\frac{3m}{2m}=9km:4km=\frac{9}{4}$$
Is there another strategic approach to solve this PS question? Can any experts help, please? Thanks!
Hi AAPL,

Once we know that a = 3k, c = 2k, b = 3m and d = 2m, then...
Area of rectangle A = ab = (3k)(3m) = 9km
Area of rectangle B = cd = (2k)(2m) = 4km

So, the ratio of the rectangle A's area to the rectangle B's = 9km/4km = 9/4

Cheers,
Brent

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by [email protected] » Mon Mar 19, 2018 5:47 am
AAPL wrote:The rectangle A has a (width) and b (height) and another rectangle B has c (width) and d (height). If a/c = b/d = 3/2, what is the ratio of the rectangle A's area to the rectangle B's?

A. 3/2
B. 3/4
C. 9/2
D. 9/4
E. 27/8
We can let a = b = 12.

We can let c = d = 8.

The area of rectangle A is 12 x 12 = 144.

The area of rectangle B is 8 x 8 = 64.

The ratio of the area of rectangle A to that of rectangle B is:

144/64 = 18/8 = 9/4