Take Home part 5

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

Thank you so much for answering my question so thoroughly!