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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)