Question

Find the length of the third side. If necessary, round to the nearest tenth. 12 18

Answer 1

Answer (assuming that the shape is a right triangle):

If looking for the hypotenuse: 21.63

If looking for one leg, given other leg is 12, and the hypotenuse is 18: 13.42

Step-by-step explanation:

Given the length of two sides of a right triangle, we can use the pythagorean theorem to find the length of the third side. The pythagorean theorem is $a^{2} + b^{2} = c^{2}$ or $c=\sqrt{(a^{2} + b^{2})}$. Given this question, I do not know what side of the triangle the problem is looking for, I would assume the hypotenuse, so let's do that first.

$c = \sqrt{(12^{2} +18^{2})} \\c = \sqrt{468} \\c = 21.63$

Or we can manipulate the equation to find different scenarios of possible legs. Such equation that can be used is $a = \sqrt{c^2 - b^2}$, where c is the hypotenuse.

Only one scenario is possible, with the hypotenuse being 18 because the hypotenuse cannot be less than one of the legs, or that leg basically becomes the hypotenuse because such side is the largest (12 < 18).

So our last scenario is, if we are looking for one leg, given other leg is 12, and the hypotenuse is 18.

$a = \sqrt{18^2-12^2} \\a = \sqrt{180} \\a = 13.42$

These are our possible answers.