C2- Trigonometry Question

I've attached the Q, it's part (a) that I need help with- Thanks!

I've attached the Q, it's part (a) that I need help with- Thanks!

ok, so i'll let the angle MON = a, where a is in radians.
This gives
perimeter = 2r + ra
(because the length of an arc is radius times angle in radians)
and the perimeter = 100, so
2r + ra = 100.
a is not in the final expression, so rearrange to get:
a = (100-2r) / (r)

now find A. area of a sector is:
A = 1/2 r^2 a.

now sub in the value we previously found for a:
A = 1/2r^2((100-2r)/r)

if we multiply out we get:
A = (50r^2 - r^3) /r = 50r - r^2

hope that helps.

The general policy on this forum is to not provide the OP with the full solution but rather hints that he/she can work from there.

oops, i get a bit carried away sometimes... these are good practice for me too!