Question

Find the length of the missing side.

The ratio of the sides of a right triangle is 1:2:8. The perimeter is 88 units. What is the length of the hypotenuse?




_________ units. ​

Answer 1

Answer: 64

Explanation:

Answer 2

well, the hypotenuse is clearly the largest side, so hmmm we know the perimeter or sum of all three sides is 88, so to get the 1:2:8 ratio, let's divide 88 by (1 + 2 + 8) and distribute accordingly.

`\stackrel{leg}{1}~~ : ~~\stackrel{leg}{2}~~ : ~~\stackrel{hypotenuse}{8} ~~ \implies ~~ \stackrel{leg}{1\cdot (88)/(1+2+8)}~~ : ~~\stackrel{leg}{2\cdot (88)/(1+2+8)}~~ : ~~\stackrel{hypotenuse}{8\cdot (88)/(1+2+8)} \\\\\\ \stackrel{leg}{1\cdot (88)/(11)}~~ : ~~\stackrel{leg}{2\cdot (88)/(11)}~~ : ~~\stackrel{hypotenuse}{8\cdot (88)/(11)}~~\implies ~~\stackrel{leg}{8}~~ : ~~\stackrel{leg}{16}~~ : ~~\stackrel{hypotenuse}{\text{\LARGE 64}}`