Exercise 20 Page 642

If the scale factor of two similar figures is ab, then the ratio of their areas is a^2b^2. With this in mind, let's consider the figures given in the exercise, and their areas. We will begin by calculating the ratio of the areas. Ratio of the Areas: 1.00/1.44 Let's simplify the given quotient.

1.00/1.44

ExpandFrac

a/b=a * 100/b * 100

100/144

ReduceFrac

a/b=.a /4./.b /4.

25/36

After simplifying, we found that the ratio between the areas of the triangles is 2536. We know the ratio is equal to a^2b^2, where ab is the scale factor of these two similar triangle. a^2/b^2 = 25/36 Let's simplify to find the scale factor ab.

a^2/b^2 = 25/36

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(a^2/b^2)=sqrt(25/36)

SqrtQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

sqrt(a^2)/sqrt(b^2)=sqrt(25)/sqrt(36)

WritePow

Write as a power

sqrt(a^2)/sqrt(b^2)=sqrt(5^2)/sqrt(6^2)

SqrtPowToNumber

sqrt(a^2)=a

a/b=5/6

We found that the scale factor of the figures is 56.