# Math Help - Constructing a Segment

1. ## Constructing a Segment

Given a segment of length a, show two different ways for constructing a segment of length (i) (square root of (19)) * a and (ii) a * (square root of (2/3))

2. Originally Posted by MATNTRNG
Given a segment of length a, show two different ways for constructing a segment of length (i) (square root of (19)) * a and (ii) a * (square root of (2/3))
Start by assembling a checklist of techniques for constructing segments whose length is some multiple of $a$. For example, can you construct one with length $ka$ (where $k$ is a whole number)? What about $a/k$? ... or $\sqrt2a$? What about $\sqrt ka$ for other values of $k$? (Think of a right-angled triangle in which two sides are known multiples of $a$. What will be the length of the hypotenuse?)