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555-605 Level|   Geometry|      
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Schachfreizeit
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A small, rectangular park has a perimeter of 560 feet and a 16 Dec 2022, 08:37
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sleekmover
The fastest way:

we know 560 is an integer (no fraction) and hence probability of sides of rectangle being integer is quite high
200 is diagonal - recognizing it from pythagorean patterns it seems to be a multiple of 10 (10 - 8 - 6)
= 10 * 2 * 10
hence other sides of the pythagorean triplet will be:
8 * 2 * 10
and
6 * 2 * 10
= 160
= 120
bingo - (160 + 120 ) * 2 = 560
hence area = 160 * 120 = 19200
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"200 is diagonal - recognizing it from pythagorean patterns it seems to be a multiple of 10 (10 - 8 - 6)
= 10 * 2 * 10"

I don't quite understand this, can someone explain it to me?
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A small, rectangular park has a perimeter of 560 feet and a 16 Dec 2022, 15:59
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Schachfreizeit
sleekmover
The fastest way:

we know 560 is an integer (no fraction) and hence probability of sides of rectangle being integer is quite high
200 is diagonal - recognizing it from pythagorean patterns it seems to be a multiple of 10 (10 - 8 - 6)
= 10 * 2 * 10
hence other sides of the pythagorean triplet will be:
8 * 2 * 10
and
6 * 2 * 10
= 160
= 120
bingo - (160 + 120 ) * 2 = 560
hence area = 160 * 120 = 19200

"200 is diagonal - recognizing it from pythagorean patterns it seems to be a multiple of 10 (10 - 8 - 6)
= 10 * 2 * 10"

I don't quite understand this, can someone explain it to me?
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Hi Schachfreizeit,

It's important to remember that nothing about a GMAT question is ever 'random' - the wording and numbers/data are always carefully chosen. Thus, you can sometimes use the 'design' of a prompt to your advantage and spot the built-in patterns that are often there.

Here, notice how ALL of the numbers are relatively 'nice', round numbers - even the diagonal is a nice number (and that doesn't happen very often when dealing with rectangles).... Since the answer choices are also round numbers, it's likely that the triangles that are 'hidden' in this rectangle are based on one of the common right-triangle patterns (in this case, the 3/4/5 - since 200 is a multiple of 5).

Using that knowledge to our advantage, IF we had a 3/4/5 and the diagonal was 200, then that would be '40 times' 5... so the other two sides would be 40 times 4 and 40 times 3: 160 and 120. With those two side lengths, we'd have a perimeter of 2(160) + 2(120) = 560... and that is an exact MATCH for what we were told, so this MUST be the situation that we're dealing with.

At this point, the area can be calculated easily enough: (L)(W) = (160)(120) = the answer

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com
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A small, rectangular park has a perimeter of 560 feet and a 13 Dec 2023, 21:19
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I was wondering, as the diagonal is a multiple of both 5 and 25, how can we be sure that it's a 3,4,5 right triangle triplet, and not a say 7,24,25?


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A small, rectangular park has a perimeter of 560 feet and a 14 Dec 2023, 02:44
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TargetMBA007
I was wondering, as the diagonal is a multiple of both 5 and 25, how can we be sure that it's a 3,4,5 right triangle triplet, and not a say 7,24,25?


EMPOWERgmatRichC KarishmaB
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You are much more likely to see 3-4-5 or 5-12-13 (and their multiples) than any other triplet. So I will first check whether 3-4-5 works

The legs have to add up to 280 and the side 5 should be 200 (the diagonal). So the multiplier here is 40.
The sum of the legs in this case would be 3+4 = 7 and since multiplier is 40, we get the sum as 280. It works. So I know the other two sides are 3*40 and 4*40.

If I were to find that it doesn't, I would then worry abt 7-24-25
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A small, rectangular park has a perimeter of 560 feet and a 14 Dec 2023, 11:58
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TargetMBA007
I was wondering, as the diagonal is a multiple of both 5 and 25, how can we be sure that it's a 3,4,5 right triangle triplet, and not a say 7,24,25?


EMPOWERgmatRichC KarishmaB
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Hi TargetMBA007,

One of the great aspects of the Quant patterns that you will see on the GMAT is that with just a little bit of work, you can prove that they're in the question that you're facing. You bring up a valid point with this prompt: since the diagonal is 200, that COULD potentially be a 3/4/5 or 7/24/25 right triangle. Since a 3/4/5 is far more common on the GMAT, we should first check to see if that is the one we're dealing with in this prompt. With just a bit of Arithmetic, you can determine the lengths of the two sides of the rectangle IF we're dealing with a 3/4/5 x 40 and see if those results line up with the other information that you're given. If the results match, then you have the answer to the question; if the results do not, then you know that it's not a 3/4/5 - and you try something else.

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A small, rectangular park has a perimeter of 560 feet and a 14 Dec 2023, 22:02
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Thanks KarishmaB EMPOWERgmatRichC

That makes complete sense.
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A small, rectangular park has a perimeter of 560 feet and a 07 Jan 2025, 03:34
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