Posted by **chica** on Monday, November 29, 2010 at 10:13pm.

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 -
**Reiny**, Monday, November 29, 2010 at 10:58pm
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 -
**big boss**, Tuesday, July 24, 2012 at 10:36am
6/4 = 9/6 6^2 =36

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