Can the sides of a triangle have lengths 39, 15, and 25?

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Answer 1 · 2016-01-23T19:42:22

No.

If we will apply the Pythagoras theorem, we know the hypotenuse is the greatest length in all three sides. Then,

${(h y p o t e ν s e)}^{2} = {(b a s e)}^{2} + {(h e i g h t)}^{2}$ $(hypotenuse)^2 = (base)^2 + (height)^2$

$h^{2} = 15^{2} + 25^{2}$ $h^2 = 15^2 + 25^2$

$h^{2} = 225 + 625$ $h^2 = 225 + 625$

$h^{2} = 850$ $h^2 = 850$

$h = \sqrt{850}$ $h = sqrt(850)$

$h = 29.154$ $h = 29.154$

$h cancel(= ) 39$

Hence, a triangle cannot have three sides of length 39, 15 and 25.