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# Take Home part 5

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How big of a square can you fit inside a right triangle with legs 5cm and 12cm long? How would you finish this problem after you find the third leg's value is 13cm long?

Nov 29, 2018
edited by SydSu22  Nov 29, 2018

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Nov 29, 2018
edited by CPhill  Nov 30, 2018
edited by CPhill  Nov 30, 2018
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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
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Thank you so much for answering my question so thoroughly!

SydSu22  Dec 1, 2018