Given that the hypotenuse of a right-angled triangle is 41cm, and the sum of the sides of the triangle is 49cm, How do you find the lengths of the other two sides?

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Answer 1 · 2015-11-09T15:55:34

9 and 40

Let #x# be the length of 1 of the missing sides
=>#49 - x# is the length of the other missing side

By pythagorean theorem, we have

#x^2 + (49 - x)^2 = 41^2#

#x^2 + 2401 - 98x + x^2 = 1681#

#2x^2 - 98x + 2401 - 1681 = 0#

#2x^2 -98x + 720 = 0#

#x^2 - 49x + 360 = 0#

#(x - 9)(x - 40) = 0#

#=> x = 9, x = 40#

If we select any of the two values of #x# and compute for the other side given #49 - x#, we will get the unselected value