In the diagram to the below, the value of x is closest to which of the

\(√3.33\) = \(1.8\)
1.8 is closed to \(√3\). So the correct choice is C, actually.

How is \(√3.33\) = \(1.43\)?

\(1.4^2 = 1.96\)
\(1.5^2 = 2.25\)
\(1.8^2 = 3.24\)

IMO ans is 1

Its an iso . triangle bcoz it has 2 equal sides.
One of the angle is 45 so the other one is also 45( same sides)

Its a 45 45 90 triangle.
The sides of 45 45 90 triangles are in ratio of 1 1 root 2.
Hypo is root 2 therefore x is 1

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Hi sir, I think its closer to \(\sqrt{3}\).
\(\sqrt{3}\)=1.7. Your answer is 1.8. It is closer to 1.7 than 2.

Anyways my working is as follows -
\(2 = (\frac{x}{\sqrt{2}})^2 + (x - \frac{x}{\sqrt{2}})^2\)
\(or, 2 = 2x^2 -\frac{2x^2}{\sqrt{2}}\)
\(or, 1 = x^2 - \frac{x^2}{\sqrt{2}}\)
\(or, x^2 = \frac{\sqrt{2}}{(\sqrt{2}-1)}\)
\(or, x^2 = 1.4/0.4 = 3 (approx)\)
\(or, x = \sqrt{3}\)

Yes obviously
I don't know what came of me
Must have not seen that option of root3 at all! - corrected that - thanks

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My calculator gave me wrong info (value of root 3.33). I was convinced with that wrong value (1.43) because i already know that the correct choice is C.

Edited the first comment..

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I believe that the question was created by Manhattan Prep to illustrate strategic guessing (I could be wrong, it was a while ago). Also, since we are estimating, we can make some approximate guesses.

I’m a triangle, the sides of a triangle are, in a sense, proportional to the angles of the triangle. The sides are in fact in a constant proportion to the Sine of each angle’s degree measure - the angle opposite each Side

Side a / (Sin Angle Opp a) = Side b / (Sin Angle Opp b) = Side c / (Sin Angle Opp c)

(1st) given we have an isosceles triangle, the other 2 angle measures both equal = (135/2) = 67.5 degrees


(2nd) The “Sine” Proportion can be taken. For each side and its opposite angle, the following proportion holds true:

Sqrt(3) / (Sine 45 deg.) = (X) / (Sine 67.5 deg.) = (X) / (Sine 67.5 deg.)


The Sine of 45 degrees = (1) / (sqrt(2))

We can use the Sine of 60 degrees to approximate the Sine of 67.5 degrees, since it easier to find and since 60 degrees is close to 67.5 degrees

The sine of 60 degrees = sqrt(3) / 2


Substituting we have:

[ sqrt(2) ] / [ 1/sqrt(2) ] = [ x ] / [ sqrt(3) / 2]

In the right hand side of the equation, the square root of 2 squared = 2——-you are left with:


2 = (2x) / (sqrt(3))

—cancel the 2 in the NUM on each side of the equation—

1 = X / (sqrt(3))

-cross multiply-

X = sqrt(3)

Since this is only an approximation and not the actual value or X, I suspect there are other ways to estimate the answer. It’s too coincidental that the estimate found happened to be the exact value of the correct answer approximation.

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For some reason the image is not visible ... Uploading here once more:



Hope this helps.

I had no idea how to solve this in a methodological way so I took an educated guess. In a 45-45-90 triangle, the largest side is √2 times the smallest side. The smallest side in our question is √2, so we know that the largest side (2 in our case) cannot be 2 (√2*√2) since this is not a 45-45-90 triangle. The largest side will have to be less than 2 and obviously more than √2 (the side opposite the smaller angle). We're only left with option C here. Is this approach correct?