If the smaller sides of a right triangle is 1/2 the length of the corresponding sides of another right triangle what is the ratio of the length of their hypotenuse.

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Let the two right triangles have sides `a, b, c` and `a', b', c'` where `c^2 = a^2 + b^2` and `c'^2 = a'^2 + b'^2` .

It is known that `a/a' = 1/2` and `b/b' = 1/2`

`c^2/(c'^2) = (a^2 + b^2)/(a'^2 + b'^2)`

= `((2a')^2 + (2b')^2)/(a'^2 + b'^2)`

= `(4*(a'^2 + b'^2))/(a'^2 + b'^2)`

= 4

**The ratio of the length of their hypotenuse is 1/4**

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