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Let the bottom left vertex of the right triangle lie at (0,0).....so.....the square will touch two sides of the triangle

Let the height of the right triangle = 5 and the base length = 12

And the endpoints of the hypotenuse lie at (0,12) and (5,0)

And the equation of the line conecting these two points is given by :

y = -(12/5)x + 12 (1)

And the diagonal of the square will be the segment lying on the line y = x (2)

Find the x coordinate intersection of (1) and (2) ..... this will be the length of the side of the square

So we have

- (12/5)x + 12 = x add -(12/5) to both sides

12 = (17/ 5) x multiply both sides by 5/17

60/17 units = the side of the square

CPhill
Nov 30, 2018