In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?

Guest Apr 10, 2019

#2**+2 **

A "slick way" to answer this question, is to label the three sides of the triangle, \(x, y, z\) . Then, we have \(x^2+y^2+z^2=1800\), but we know that \(x^2+y^2=z^2\) in a right triangle, so we have \(z^2+z^2=1800\) or \(2z^2=1800\), and \(z^2=900, z=30\) .

Thus, the length of the hypotenuse is \(\boxed{30}\) .

tertre Apr 10, 2019

#1**+1 **

18 24 30 is a possibility. (a multiple of 3-4-5 common rt triangle) Hypotenuse = 30

ElectricPavlov Apr 10, 2019

#2**+2 **

Best Answer

A "slick way" to answer this question, is to label the three sides of the triangle, \(x, y, z\) . Then, we have \(x^2+y^2+z^2=1800\), but we know that \(x^2+y^2=z^2\) in a right triangle, so we have \(z^2+z^2=1800\) or \(2z^2=1800\), and \(z^2=900, z=30\) .

Thus, the length of the hypotenuse is \(\boxed{30}\) .

tertre Apr 10, 2019