Question

If the length and width of a rectangle each triple​, what happens to the area of the​ rectangle?

Answer 1

Answer: the area multiplies by 9

In other words,
new area = 9*(old area)

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Consider this example:
we have a rectangle that has...
width = 10
length = 12
the area then then 120 since length*width = 12*10 = 120

If we triple each dimension, then we have these new dimensions
width = 30
length = 36
which leads to the new area 36*30 = 1080

Note how the ratio of the areas is 1080/120 = 9
telling us that the new area is 9 times that of the old one

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In terms of algebra
L = old length
W = old width
A = L*W = old area

3L = new length
3W = new width
B = new area
B = (3L)*(3W) = 9*(LW) = 9*A

So B = 9*A tells us that the new area is 9 times the old area

This rule works for any shape. It doesn't have to be a square or a rectangle.