Exercise 37 Page 425

We are told that the triangles illustrated on the diagram are similar and are asked to find the values of x and y. Let's name the vertices of the triangles for future reference.

First, we need to calculate the scale factor from the smaller triangle to the bigger one. Then we will use it to find the values of x and y.

Scale Factor

Let's recall that a scale factor is the ratio of the lengths of the corresponding sides of the polygons. From the diagram we know that EF corresponds to AC. Calculating the ratio of their lengths, we can find the scale factor from the smaller triangle to the bigger one.

EF/AC=18/24= 3/4

Value of x

Side ED corresponds to BC and the ratio of their lengths is equal to the scale factor. ED/BC= 3/4 Let's substitute ED with x-6 and BC with 39 and solve the equation for x.

ED/BC=3/4

SubstituteII

ED= x-6, BC= 39

x-6/39=3/4

MultEqn

LHS * 39=RHS* 39

x-6=117/4

CalcQuot

Calculate quotient

x-6=29.25

AddEqn

LHS+6=RHS+6

x=35.25

We got that the value of x is 35.25.

Value of y

To determine the value of y, we need the find the length of DF. From the diagram, we can see that DF corresponds to AB. The ratio of their side lengths is equal to the scale factor of the triangles. DF/AB= 3/4 Let's substitute DF with y and AB with 27 into the equation and solve it for y.

DF/AB=3/4

SubstituteII

DF= y, AB= 27

y/27=3/4

MultEqn

LHS * 27=RHS* 27

y=81/4

CalcQuot

Calculate quotient

y=20.25

Therefore, the value of y is 20.25.