Answer:
20
Explanation:
Two ways to solve this: We know the triangle in question is an isoceles right triange. Brute force is we know its hypotenuse = 5*sq root of 8 or 14.142136. applying pythagoras, this squared = 2 times leg length squared. So, 14.142136 squared = 200 so each leg = sq. root of 100 or 10. So, sum of lengths = 20.
The short cut is to recognize that 5* sq. root of 8 = 10 times the sq. root of 2 (because 8 = 2 cubed). So the hypotenuse becomes 10 times sq root of two and in an isoceles triangle, this multiplier (10) is always the short legs' length. So sum is 10+10.
