Let's do this question, two opposite sides of a square given by the equations, three X plus four Y
minus 10 is equal to zero and three X plus four Y plus 20 equals zero.
Find the length of the diagonal of the square.
All right.
What's the video?
Give it a try and then let's do it together.
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We're back.
Let's do it together.
So let me draw a rough sketch over here.
I have a square over here.
Let me name it as A, B, C, D.
OK, so now you can notice that the side of the square will be equal to the distance between two sides.
Right.
So, for example, if I find the distance between A, B and C, that would be equal to the side of the
square.
Right.
Because all the sides are equal.
So I just need to find the distance between two sides.
All right.
So I am given over here to equations of lines.
Right.
That are opposite to each other.
And we know that opposite sides in a square are parallel to each other because a square is a parallel.
Now we know how to find the distance between two parallel lines.
That would be C one minus two divided by square root of A squared plus B square.
Right.
And you always take the positive value.
So let's apply that over here.
You get twenty minus minus ten divided by square root of three squared plus four square.
Right over here you have 20.
That's your C one.
And over here you have minus 10.
That's your C two.
Right.
So twenty minus minus ten divided by root of three squared plus four square threes.
Your eight and four is your beat.
Now this simplifies to 30 divided by five which is equal to six.
Now if your option in the question was six, don't hurry to mark the answer.
Six, because over here we are asked to find the length of the diagonal of the square.
Right?
So if the side of the square is six units, then the diagonal would be six root two.
Right.
Why is that?
So we have to save six.
And this angle is a 90 degree angle.
Therefore, Asper Pythagoras's theorem this side over here, which is a diagonal, will be root of six
squared plus six square, which is equal to six through to.