Ratio and proportion

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

Weekly Problem 37 - 2007
This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

A brief introduction to PCR and restriction mapping, with relevant calculations...

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

Weekly Problem 3 - 2007
What is the ratio of the area of the table covered twice, to the uncovered area?

A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?