# Geometry

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Rectangles

The ratio of the length to the width of one rectangle is proportional to the ratio of the length to the width of a smaller rectangle. Describe the circumstances for which this proportion involves a geometric mean.

• Geometry -

if x is a geometric mean between two numbers a and b, then
x/a = b/x
x^2 = ab
x = √(ab)

if the length of the small one is l
and its width is w

then the width of the larger has to be l
and the length has to be l2
so l/w = l2/w
w = √(l*l2)

e.g. small rectangle is 4 by 6, larger is 6 by 9
notice 4/6 = 6/9
and 6^2 = 4*9

e.g. first rectangle

• Geometry -

6/4 = 9/6 6^2 =36

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