Question 238960
You can start with the Pythagorean theorem:
1) {{{c^2 = a^2+b^2}}} and ...
2) {{{a^2+b^2+c^2 = 300}}} "The sum of the squares of the lengths of the three sides of a right triangle is 300 sq.cm."
Solve equation 2) for {{{c^2}}}
2a) {{{c^2 = 300-(a^2+b^2)}}} Substitute {{{a^2+b^2 = c^2}}}
2b) {{{c^2 = 300-c^2}}} Add {{{c^2}}} to both sides.
2c) {{{2c^2 = 300}}} Divide both sides by 2.
2d) {{{c^2 = 150}}} Take the square root of both sides.
2e) {{{c = sqrt(150)}}} Simplify, noting that {{{sqrt(150) = sqrt(25*6)}}}.
2f) {{{highlight(c = 5*sqrt(6))}}}cm.
The length of the hypotenuse is {{{5*sqrt(6)}}}cm.