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Let triangle XOY be a right-angled triangle with XOY being 90 degrees. Let M and N be the midpoints of legs OX and OY respectively. Given that XN=24 and YM=31, find XY (aka the hypotenuse).

 Sep 10, 2020
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Let triangle XOY be a right-angled triangle with XOY being 90 degrees. Let M and N be the midpoints of legs OX and OY respectively. Given that XN=24 and YM=31, find XY (aka the hypotenuse).

 

OX => a       OY => b

 

242 = (b/2)2 + a2

 

576 - (b/2)2 = a2

~~~~~~~~~~~~~~~~

(a/2)2 = 312 - b2

 

a2 / 4 = 961 + b2

 

a2 = 3844 - 4b2                   a2 = 358.13333333

~~~~~~~~~~~~~~

576 - b2 / 4 = 3844 - 4b2

 

b2 = 13072 / 15                  b2 = 871.4666667

 

XY = sqrt( a2 + b2 ) = 35.0656527   smiley

 Sep 11, 2020
edited by jugoslav  Sep 11, 2020
edited by jugoslav  Sep 11, 2020
edited by jugoslav  Sep 11, 2020
edited by jugoslav  Sep 11, 2020
edited by jugoslav  Sep 11, 2020
edited by jugoslav  Sep 11, 2020
edited by jugoslav  Sep 11, 2020

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