a Multiply the equation by the denominator in the fraction on the left-hand side.
B
b Multiply the equation by the denominator in both fractions.
C
c If you divide the number of inches by the number of months, you get a proportion describing the rate of growth.
D
d There are two similar triangles in the diagram.
A
a y=3.25
B
b y=- 2
C
c x≈ 4.66 inches
D
d x=4 units
Practice makes perfect
a To solve the equation, we should multiply both sides of the equation by the denominator of the fraction on the left-hand side. In doing so, we can eliminate this fraction.
c Using the given information, we can write the following equation describing how Sam grows in inches per month.
inches/months=1 34/4 12 ⇔ inches/months=1.75/4.5In one year there is 12 months so if we call the number of inches Sam can grow in one year x, we get the following equation.
x/12=1.75/4.5
Let's solve this equation for x.
d From the diagram, we can identify a pair of congruent corresponding angles and a shared angle in two triangles.
Since the triangles have two pairs of congruent angles, we can say by the AA Similarity condition that they are similar. In similar shapes the ratio between corresponding sides is constant. By separating the triangles, and identifying corresponding sides, we can write an equation that includes x.
