Exercise 32 Page 605

Let's analyze the given triangles.

First, notice that two angles of the bigger triangle are congruent to two angles of the smaller triangle. Therefore, by the Angle-Angle (AA) Similarity Postulate these triangles are similar. △_(Bigger) ~ △_(Smaller) We are given the lengths of the altitudes of the triangles. Recall that if two triangles are similar, the lengths of their corresponding altitudes are proportional to the lengths of their corresponding sides. Therefore, we can write the following proportion. 8/16 = 11/x Let's solve it!

8/16 = 11/x

▼

Solve for x

ReduceFrac

a/b=.a /8./.b /8.

1/2 = 11/x

MultEqn

LHS * 2=RHS* 2

1/2 * 2 = 11/x * 2

FracMultDenomToNumber

a/2* 2 = a

1 = 11/x * 2

MoveRightFacToNum

a/c* b = a* b/c

1 = 11 * 2/x

Multiply

Multiply

1 = 22/x

MultEqn

LHS * x=RHS* x

1 * x= 22/x * x

OneMult

1* a=a

x= 22/x * x

FracMultDenomToNumber

a/x* x = a

x = 22