Rectangle

[Videoorchard]

Hey,

I have a question regarding a problem in the geometry guide. The question is taken from Guide3: chapter 3: Problem Set: 14 Q.

Here in the figure, since the corners of what looks like a rectangle or square is 90, and a diagonal bisects them, i.e 90/2=45 degree each, why can't we assume the value of X and Y to be 45 each? Am i missing something? :)


Thank you for answering! :)

[n00bpron00bpron00b]

I hope I am answering the right question :). Is it the one where we have to compare Quantity A - "x" and Quantity B - "y" - and the diagram contains variables "x" & "2y" placed on either side of the line :D


1st - Don't fall into the trap of assuming on geometric questions - proceed ahead on the basis of what information is given and what can be deduced from it

2nd - It is no where stated that the diagram is an rectangle or square or if the bisecting line is a diagonal

Some of the ways be can prove it as an square -
-> All angles should be 90
-> All sides must be equal or a
Rhombus with two angles 90 and so on

Similarly, for rectangle
-> All angles should be 90
-> Opp sides equal and so on

Now the solving part -

a) We cannot assume angle x and y as 45 each, just because the line looks like a diagonal, for the matter of fact the given diagram may not even be a rectangle or square. We have no valid basis to assume anything.

b) Start with what is given - i.e
If you notice the upper right 90 degree triangle -

-> One angle is 90 (given)
-> One side of 90 degree angle has length = "1"
-> Side opp the 90 degree angle has length = "2"

We can use the Pythagorean theorem to find the 3rd side

Let the third side be "p"
(1)^2 + (p)^2 = (2)^2
1 + p^2 = 4
p^2 = 3
p = square root of 3

Okay, now we have a triangle with three lengths
1, square root of 3 and 2

If you notice these lengths (1,sq root 3, 2) are nothing but 30-60-90 special right triangle.

30 - 60 - 90 => lengths => 1,sq.root 3,2

From above we can conclude - the angle opposite ("x") side length 1 is 30 degrees

so x = 30 degrees

If x is 30 degrees then 2y is 90-30 = 60 degrees
If 2y = 60
y =30

x = 30
y = 30

"C"

[Videoorchard]

Hey Nooob :)

Thank you for clearing my doubts! :) Geometry figures can be diabolical at times :) Also do you know what "figure is drawn to scale/drawn as accurately possible" mean in the geometry questions?

[tommywallach]

Great answer from noob, as usual! As for your follow-up, I answered that on a separate thread for ya! : )

[Videoorchard]

Thank you tommy for clearing my doubts! :)

[tommywallach]

Glad to help!