Question 1029298: Two similar figures have areas of 56 sq in and 87 sq in. A side of the smaller figure is 12 in. Find the corresponding side. Found 2 solutions by Edwin McCravy, josgarithmetic:Answer by Edwin McCravy(20054) (Show Source):
Areas of similar figures vary as the squares of the sides, so
Cross-multiply:
Divide both sides by 56:
Since the other figures are rounded to the
nearest whole number, we probably should
round the corresponding side of the larger
to 15 inches.
Edwin
Imagine you have rectangles. One is length 12 and the other is unknown length, but you are given the rectangles are similar.
SMALL Rectangle
dimensions 12 and x
LARGE Rectangle
dimensions 12k and kx
; the k because this is a proportionality constant, because the length of the rectangles ARE IN PROPORTION because the two rectangles ARE SIMILAR.
Goal is to find 12k, which is the length for the corresponding side on the larger rectangle.
The system to solve is this:
from which you should see the substitution to do;
The corresponding side length on the larger figure is ; and you could rationalize the denominator and simplify if you want.
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