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.
1 Answer | Add Yours
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)`
The ratio of the length of their hypotenuse is 1/4
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes