# math

posted by Esther

square x has an area of 100 square units. Square Y has a perimeter that is half of the perimeter of square x. What is the area of square y?

1. Damon

each side of x is 10 units since it is square
then each side of y must be 5 units
and its area is 25 square units

In fact the ratio of areas of any two similar figures is the square of the linear scale ratio between them.

2. helper

Square X, s = side
Area, A = s^2
100 = s^2
Take square root of both sides
10 = s

Square X, s = side
Perimeter, P = 4s
s = 10
P = 4(10)
P = 40

Square Y, s = side
Perimeter of Sq. Y = 1/2 Sq. X
Perimeter of Sq X = 40,
P = 1/2 (40) = 20
P = 4s
20 = 4s
s = 5

Square Y, side = s
Area, A = s^2
s = 5
A = 5^2
A = 25 sq units

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