Question: Tilted Triangle Area

Comment on Tilted Triangle Area

Hi Brent, you state that the Enlargement factor is 6 given that the ratio of the new triangle is 1:√3:2. With the largest side being 12. We find this enlargement factor via 12/2=6.

However, if the smallest side is 5. Wouldn't the Enlargement factor in this case be 5/1 = 5. From my understanding, we can only have one enlargement because it should apply to all lengths in the ratio. As a result, we have two separate enlargement factors.

I appreciate you clarifying.
gmat-admin's picture

Good question.

The side with length 5 is just a PORTION of the blue 30-60-90 triangle that we draw at 0:40 in the video.

So the length of the side opposite the 30° will be LONGER than 5.

Since we don't know the exact length of the side opposite the 30°, we can't use that to determine the enlargement factor.

Does that help?


That makes sense! I did not take into account that the conceptualized 30-60-90 triangle will have a longer base.

There are so many tricky things to keep track of in Geometry. Changing one length/angle in a diagram has an inverse effect on one or multiple other things in the diagram! Thanks again for clarifying.
gmat-admin's picture


I attempted to say that 12 was the base then i rotated the triangle and then drew a line straight down from c to 12. Does this line neccesarily form a right angle?
gmat-admin's picture

Drawing a line from C to the side with length 12 (side AB) is a valid approach as long as that line is PERPENDICULAR to side AB.
That way, the nice line will represent the height of the triangle.

If you do that, you'll find that you have a 30-60-90 right triangle, in which side CB (with length 5) is the hypotenuse. So, you can use that information to find the height.

If you do that, you'll find that the height will be 5√3/2

In your approach, the base has length 12

So, the area = (12)(5√3/2)/2 = 15√3



Since this is a right triangle, why can't I just use Pythagorean theorem to do this?

I got 5^2 + b^2= 12^2
Simplify- Square root of 119

Simply plug it in the formula, I for (5 sqr 119)/2

Could you please clarify?

Thank you
gmat-admin's picture

We can't use the Pythagorean Theorem here, because we only know the length of ONE side of the RIGHT triangle: the hypotenuse AB.

Notice that 5 is not the length of another side of the right triangle.
5 is only PART of the side that comprises another side.

Does that help?


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