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!

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

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You could also just pick numbers.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!

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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Hi AAPL,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!

Your solution is perfect.

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

Answer: D

Cheers,

Brent

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**Posts:**6362**Joined:**25 Apr 2015**Location:**Los Angeles, CA**Thanked**: 43 times**Followed by:**25 members

We can let a = b = 12.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 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

Answer: D

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