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?

Question

7403 views around the world

You can reuse this answer
Creative Commons License

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