Exercise 39 Page 568

We are given the measures of the angles in a pair of similar triangles. We also know the side lengths. We want to find the value of x. Let's make a picture of this triangles and mark the known values on it.

Let's begin by recalling that in similar triangles corresponding sides are proportional. With this information, we can create a proportion by writing the ratios of the lengths of a corresponding sides.

Ratio of Corresponding Sides
3/x-0.46
3.25/x
4.23/x+1.81

To find the value of x, we will use only two of the above ratios. Let's write a proportion using the first and the second ratio. 3/x-0.46 = 3.25/x Now, we will solve the equation for x. To do this we will use a cross multiplication. When using cross multiplication, we treat x-0.46 like a single term.

3/x-0.46=3.25/x

CrossMult

Cross multiply

3x=(x-0.46)* 3.25

▼

Solve for x

Distr

Distribute 3.25

3x=3.25x-1.495

SubEqn

LHS-3.25x=RHS-3.25x

-0.25x=-1.495

DivEqn

.LHS /(-0.25).=.RHS /(-0.25).

x = - 1.495/- 0.25

DivNegNeg

- a/- b=a/b

x = 1.495/0.25

CalcQuot

Calculate quotient

x = 5.98

RoundInt

Round to nearest integer

x≈ 6

We found that the value of x is approximately 6.