Question

consider a swuare with side of lengh 's' and diagonal of length 'd'. write a formula expressing 'd' as a function of 's'...............is this correct: d(s) ?

Answer 1

The internal angle between two adjacent sides of the square is 90°.
The diagonal bisects this angle (This can be proved by establishing the congruency of the two triangles thus formed).
Hence, the angle between one side of the square and the diagonal is 45°.
If the length of the diagonal is d, and the length of the side of the square is s, then basic trigonometery tells us that d.cos45° = s.
Since cos45° = 1/√2 = 0.707, we have:
s = 0.707d; d = 1.414s

O.K.?