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## Comment on

Value of x## I solved as : since triangle

Now 2x corresponds to side of length 4x -3, so I took

2x= 4x -3 . when solved for x, I get x = 3/2. Please correct me as to where I'm wrong?

## In your equation, 2x = 4x -3,

In your equation, 2x = 4x -3, the x on the LEFT side does not represent the same value that x represents on the RIGHT side. So, your equation isn't valid.

Notice that, the two lengths (x+1) and (4x-3) could also be (x+3) and (4x). If we apply your strategy here, we conclude that 2x = 4x, which makes no sense.

Instead, we must us the RELATIONSHIPS between corresponding sides to solve this question.

## Thank you Brent. I have one

## Sorry, but I'm not sure what

Sorry, but I'm not sure what you're asking.

If you have a 30-60-90 triangle, and the hypotenuse has length 6, then you can conclude that the shorter leg has length 3 and the other leg has length 3√3

Does that help?

## Do you get the comments if

## Yes, I see the comments here.

Yes, I see the comments here.

## Hello Brent, I clicked on the

## Yes, I received the reply.

Yes, I received the reply.

I didn't get back to you immediately, but I always answer questions within 24 hours.

Cheers,

Brent

## Can we also use the

## We can certainly apply the

We can certainly apply the enlargement factor here.

On the shown triangle, the side with length x+1 corresponds to the side with length 1 in the BASE triangle.

So, the enlargement factor = (x+1)/1 = x+1

On the shown triangle, the side with length 4x-3 corresponds to the side with length 2 in the BASE triangle.

So, we can write: (2)(x+1) = 4x-3

Expand: 2x + 2 = 4x - 3

Solve, to get: x = 5/2

Cheers,

Brent

## Trignometry clicked me here ,

## If you remember that sin 60 =

If you remember that sin 60 = √3/2, then that will help you.

However, trigonometric ratios are beyond the scope of the GRE, so you can also just apply what you know about 30-60-90 right triangles.

Cheers,

Brent

## Since, as you've pointed out

2(side opposite 30˚) = side opposite 90˚

2(x+1) = 4x-3

and solve for x.

Not saying it's better, just another approach.

## That's a great approach! In

That's a great approach! In fact, it shaves a step off my solution!

Using similar triangles, I first wrote: (x+1)/1 = (4x-3)/2

After cross multiplying, I got: 2(x+1) = 4x-3

In your (faster) solution, you started with 2(x+1) = 4x-3

Very nice!

Cheers,

Brent

## Hi Brent, for this problem

## That approach will also work

That approach will also work (although you end up with a pretty tricky quadratic equation to solve)