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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?

 Apr 10, 2019

Best Answer 

 #2
avatar+4249 
+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 \(\boxed{30}\) .

 Apr 10, 2019
 #1
avatar+18279 
+2

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

 Apr 10, 2019
edited by ElectricPavlov  Apr 10, 2019
 #2
avatar+4249 
+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
 #3
avatar+101150 
0

Nice, tertre....!!!!

 

 

cool cool cool

CPhill  Apr 11, 2019

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