On a scale drawing of a triangular piece of land, the sides of the tri

The key here is to recognize that 5, 12 and 13 represent a Pythagorean triplet, which means the triangle in question is a RIGHT TRIANGLE

So, the drawing has sides 5 cm, 12 cm, and 13 cm . . .

. . . which means the piece of land has sides 15 m, 36 m and 39 m

Area of triangle \(= \frac{(base)(height)}{2}\)

So, the area of the land \(= \frac{(36)(15)}{2} = 270\)

Answer: D

ASIDE: Other Pythagorean triplets you should know:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

Cheers,
Brent

I can see that you've recognized that each side on the piece of land (in meters) is THREE TIMES the length each side on the drawing (in centimeters).
e.g., 15 is THREE TIMES 5, 39 is THREE TIMES 13, and 36 is THREE TIMES 12
So, it SEEMS that the area of the big triangle should be THREE TIMES the area of the small triangle.

However, when it comes to areas, there are TWO lengths involved.
For example, the area of 1x1 square is 1
If we take each side and TRIPLE it, we get a 3x3 square.
Is the area of this bigger square three times the area of the smaller square?
No, the area of this bigger square NINE times the area of the smaller square.

The same applies to this question.
If a triangle has a base of length b and a height of length h, then the area = bh/2
If the sides are TRIPLED, the new triangle has a base of length 3b and a height of length 3h, in which case the area = (3b)(3h)/2 = 9bh/2
So, the new area is NINE TIMES the area of the original triangle.

Does that help?

Cheers,
Brent

sides ; 5:12;13
or say 15:36: 39
area will be 1/2 * 15 * 36 ; 270
IMO D

GMATPrepNow
Why does this process give incorrect result?
Area in Centimetres = (5*12)/2=30
So, area in metres= 30*3=90
Ans. A
What's wrong here?

Posted from my mobile device

msu6800
well try to use the hint given within question it says that ∆ region is 5,12,13 so it implies its a right angled ∆
now given is another info that 1 cm = 3 cm so now simply multiply each side by 3 we get 15,36,39 so its 30: 60 : 90 angled ∆
since its a right angled hypotenuse will remain 39
so 1/2 * 15 * 36 = 270

hope this helps

Archit3110
I understand the solution but my question is "what is wrong in getting Area in Centimetres, and then converting centimetres in Metres? Please, check my approach to solution. Where is the wrong?
Thanks.

Posted from my mobile device

msu6800
well area is in m^2 so you have to multiply by 3 twice ; you shall get answer then by your approach..

Archit3110
Thanks a lot. Got it now.

Posted from my mobile device

Also important to note.
You can solve this as follows:

(5cm*12cm)/2 = 30cm^2
1cm =3m so 1cm^2 = 9m
30(9m)= 270m

Hi msu6800,

While your question is to Brent, I can help you with the same. In fact I made the same mistake and ended up with 90. But the key here is that the area resulting from the below highlighted portion is in \(cm^2\) and NOT \(cm\), as area, which is the product of two lengths, is as we all know is in square units.

Hence, if \(1\) \(cm\) is \(3\) \(mt\) then \(1\) \(cm^2\) will be \(3^2\) \(mt^2\) or \(9\) \(mt^2\). Plugging this info we get - \(30\) \(cm^2\) \(=\) \(30 * 9\) \(mt^2\) \(=\) \(270\) \(mt^2\)

Since 1 cm represents 3 meters, the sides, in meters, of the triangular piece of land are 5 x 3 = 15, 12 x 3 = 36 and 13 x 3 = 39. Furthermore, since 5-12-13 is a right triangle, 15-36-39 is also a right triangle. Therefore, the area of the triangular piece of land is half of the product of its legs (the two shorter sides), that is,

Area = ½ bh = ½ x 36 x 15 = 18 x 15 = 270 m^2

Answer: D
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The ratio of triangular lengths represents the Pythagorean triple. Thus 5,12, and 13 is a triangle with 13 as the hypotenuse.

Convert before the calculating area.

The area with conversation in square meters= \(\frac{1}{2}*5*3*12*3 = \) \(5*3*6*3 = 270\)

The Answer is D

Great explanation BrentGMATPrepNow. So in areas calculation, we should do convertion first for rest of calculation. Whereas if it's not areas, then we do convertion afterwards and why is that as in this question below? Thanks Brent

https://gmatclub.com/forum/on-the-map-a ... 24809.html

There's no set rule when it comes to performing the unit conversions.
It really depends on the given information.

I see thanks BrentGMATPrepNow. Problem is conversion before and after do not necessarily arrive at same answer therefore can be quite confused sometimes.

Can you give me an example of such a case?

Thought was not but they are after trying out some before and after conversion of calculations in other topics except areas. That clairfy my confusion and feeling more confident now. Thanks Brent

BrentGMATPrepNow
Should the takeaway from this problem be then that you should first convert the sides to the relevant units before calculating the area? I made the mistake of just multiplying the area by 3. Thank you and Happy Holidays

Hi woohoo921
Thanks for your query.


As you realized, correct conversion of units is a must before you mark the final answer choice. Now, for this question, “correct conversion” could be done in two ways – before finding the area and after finding the area.
There is no rule as to which one is better, but I encourage you to choose one that feels more natural to you.

Let’s see both approaches here one by one:


First approach (Before):
In this approach, we convert all given units into the desired units at the very start. In this question, it would mean finding each side of the triangular land (in m) using each side of the drawing (in cm):

• Since the dimensions of the drawing are (5) cm by (12) cm by (13) cm, the dimensions of the triangular land will be (5 × 3) m by (12 × 3) m by (13 × 3) m.
• We then just use these dimensions of the land to get its area in square meters.
  
  • Land Area = ½ × 15 m × 36 m = 270 \(m^2\).

Second approach (After):
In this approach, we first calculate the area of the drawing (in \(cm^2\)) and then use the given relationship between the land and the drawing (1 cm = 3 m) to get the area of the land (in \(m^2\)).

Step 1: Find the area of the drawing using given dimensions (in cm).

• Drawing Area = ½ × 5 cm × 12 cm = 30 \(cm^2\). ------(1)

Step 2: Use the relationship given (1 cm on drawing = 3 m on land)

• From (1), Drawing Area = 30 square centimeters
  
  • = \(30 × (1 cm)^2\)
• So, Land Area = \(30 × (3 m)^2\) = \(270 m^2\) ----(2)
  
  • Observe how we did not just have a single “cm” to convert to “m”. We have \(cm^2\), that is cm × cm. This is exactly where your mistake lies. 😊
• Finally, using (1) and (2), we can say that Land Area = \(30 × (3 meters)^2\)
  
  = 30 × (9 square meters) = \(270 m^2\).

So, both ways take us to the same correct answer!


TAKEAWAYS:

1. All the dimensions can be converted to desired units before proceeding to solve for a required quantity, OR
2. Units can be converted at the final stage as well, using the given conversion rates and keeping in mind the EXPONENT with each unit. (Here, we had 2 as the exponent on cm)

Hope this will clarify!


Best,
Aditi Gupta,
Quant Expert, e-GMAT
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