1.

Points X and Y are on sides BC and CD of square ABCD, as shown in the figure. The lengths of XY, AX and AY are 3, 4 and 5 units respectively. Then the side length of square ABCD is:

Answer» In triangle AXY, sides are `3,4, and 5`. These are Pythagoras triplets which means, triangle AXY is aright angle triangle.
Let `/_XAB = theta`
Then, `/_CXB` will also be `theta`.
As sides of a square are equal.so,
`AB =BC=>AB = BX+CX`
`=>4costheta = 4sintheta+3costheta`
`=>costheta = 4sintheta=>sintheta/costheta = 1/4 `
`tantheta = 1/4=> costheta = 4/sqrt(4^2+1^2) = 4/sqrt17`
So, `AB = 4costheta = 16/sqrt17`
so, side of the square will be `16/sqrt17`.


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