Question 621037
The pythagorean Theorem is {{{a^2+b^2=c^2}}}. If you substitute in 5 and 12 for a and b respectively you get {{{5^2+12^2=25+144=169}}}. {{{sqrt(169)=13}}}. Thus the ratios of the sides must be 5, 12, and 13. Now we know that in order to maintain this ratio we must multiply the sides by a common factor such that the perimeter equals 90. To do this we can create the following equation:
{{{5x+12x+13x=90}}}. We can further simplify this equation so it becomes {{{30x=90}}}. Now we must divide both sides of the equation by 30, so we get {{{x=3}}}. Now that we know that the common factor is 3 we can simply multiply the side length with a ratio of 13 by 3 and we get {{{13*3=39}}}. Thus, the side lengths must be 15, 36, and 39 as {{{15+36+39=90}}}. The longest side of the three is 39, so 39 is the answer.