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## Comment on

Tilted Triangle Area## Why wouldn't the answer be D?

## If angle ACB were already 90

If angle ACB were already 90 degrees, then the triangle would already be a 30-60-90 special right triangle. HOWEVER, its given sides of length 5 and 12 would not conform to the known lengths of 30-60-90 special right triangles. This means we can conclude that triangle ABC is NOT a 30-60-90 special right triangle.

## So when you extended the base

## That's correct. We just

That's correct. We just extend an imaginary line (indicated by a dotted line) along the base so we can determine the triangle's height. If we change the length of side CB (as you suggest) then we are no longer dealing with the same triangle we started with.

## Okay, and sorry again for the

I thought the height had to be greater than 6(times the square root of 3), since the base was less than 6. So I thought (like exactly what you said), extending the base would have changed the triangle we started with, and went the route I went as mentioned earlier.

I am truly appreciative of your help and these resources.

Thank you again

## The Pythagorean theorem only

The Pythagorean theorem only applies to right triangles. Since we are not told this is a right triangle, we can't use that theorem.

## Thanks for your persistence

## So when you extended the base

You stated in your response that the given triangle ABC was not a 30-60-90 special right triangle until you made it so by extending the base when looking for the height (since the sides of the lengths given did not conform until you extended the base).

So this is why I'm not understanding; for if the base had to be extended to find the height, to make a right 30-60-90 triangle (because what was given in the question was not a 30-60-90 right triangle); than, that means the base could no longer be 5 (but 6), since what was given had to changed via the extension of the base; to find the height (to therefore solve for the area).

Sorry for the beginning repeat, I wasn't finished with my initial comment before it was sent prematurely. Thank you for your help by the way; I just want to do well and am appreciative of the time spent and dedicated to these resources.

Thank you again

## We are creating a

We are creating a hypothetical 30-60-90 right triangle by extending the base (using an imaginary line). We use that hypothetical 30-60-90 right triangle to find the height of the original ABC triangle.

## lol No prob Jimmy, and Thank

## What is enlargement factor

## The "enlargement factor" is a

The "enlargement factor" is a number representing how much larger one triangle is when compared with another triangle. We use it when comparing similar triangles.

More here: https://www.greenlighttestprep.com/module/gre-geometry/video/870

And here: https://www.greenlighttestprep.com/module/gre-geometry/video/872

## Hi, I just have two question.

so, how come the base is 5, should n't be 6 to follow the special triangle 30-60-90

12/2= h/ root 3= 6/1? not 5 right? I hope u got me.

2nd question is when should use the fact that in similar triangles the ratio of any pair of corresponding sides is the same and when we should use "enlargement factor"?

## Question 1: The side with

Question 1: The side with length 5 is NOT part of a special triangle 30-60-90 triangle.

Once we CREATE a special triangle 30-60-90 triangle (by extending a perpendicular line from A down to the base), the 30-60-90 triangle has a base that's LONGER than 5.

Once we CREATE the special triangle 30-60-90 triangle, the only side we know about is the hypotenuse, which has length 12.

Question: Any time we have two similar triangles, it may be useful to apple the enlargement factor technique.

## The formula for finding the

## It's in the Geometry module,

It's in the Geometry module, here: https://www.greenlighttestprep.com/module/gre-geometry/video/865

Cheers,

Brent

## Hi Brent,

Why can't we use the pythagorean theorem to find the height. Height ends up being root 119, area is 5*root 119 / 2 choice C?

## Hi aferro1989,

Hi aferro1989,

That's a good idea, but there's one problem.

At 0:36 in the video, we create a blue right triangle.

The hypotenuse of this right triangle has length 12, BUT the length of the bottom leg is NOT 5.

The length of the bottom leg is 5 PLUS some unknown value.

Since we don't know the length of the bottom leg, we can't apply the Pythagorean Theorem.

Does that help?

Cheers,

Brent

## Thanks Brent! Still a bit

## Yes, we are using the blue

Yes, we are using the blue (artificial) triangle to determine the height (and resulting area).

This is fine, because we are certain that the triangle is a 30-60-90 triangle, AND we are certain that the hypotenuse has length 12.

Given this, we have enough information to find the height of the blue (artificial) triangle.

That said, your strategy (of applying the Pythagorean Theorem) WOULD be valid IF we had more information.

Aside: if we want to use the Pythagorean Theorem to find the length of one side, we must know the lengths of the other TWO sides.

In the case of your proposed solution, all we know is that the hypotenuse has length 12. We don't know the length of the bottom leg of the triangle.

Here's an image showing the missing measurement: https://imgur.com/j9fwDDy

Does that help?

Cheers,

Brent

## That's helpful, thank you

## Thanks Brent for all your

## To calculate the area of any

To calculate the area of any triangle, we can make any side the base.

For each side we use as base, we'll get a different height.

To see this in action, watch 4:50 to 6:00 of the video on finding the area of a triangle (https://www.greenlighttestprep.com/module/gre-geometry/video/865)

Cheers,

Brent

## Hello I didn’t understand why

## We know that the BASE 30-60

We know that the BASE 30-60-90 triangle has measurements 1-√3-2

So, for example, in the BASE 30-60-90 triangle, the hypotenuse has length 2.

The triangle in the question has been enlarged by a factor of 6

We know this because its hypotenuse has length 12

If the enlargement factor is 6, then we can find the other two lengths by multiplying the BASE triangle measurements by 6.

So, the side opposite the 30° angle has length 6 (since 1 x 6 = 6) and the side opposite the 60° angle has length 6√3 (since √3 x 6 = 6√3)

Since the side opposite the 60° angle is the height of the triangle, and the base has length 5, we now have all the information we need to find the triangle's area.

Does that help?

## Hi Brent,

In the above comment, you mentioned that the side opposite 30° angle has length 6 then it can be the base right

So by calculating the area of triangle = 1/2(b*h)= 1/2(6*6√3) = 18√3

## What you're saying is kind of

What you're saying is kind of correct (but it's referring to a different triangle)

The BLUE triangle that we created at 0:36 of the video will have the measurements 6, 6√3 and 12, which means the area of the BLUE triangle = 18√3

However, we're asked to find the area of triangle ABC, and that triangle has a base of length 5 and a height of 6√3, which means it's area = 15√3

Does that help?

## Why do you decide to use the

## Great question!

Great question!

The "enlargement factor" technique and the "equivalent ratios" technique are very closely related, and both can be used to find missing sides in similar triangles.