CPM Homework Help : CC2 Problem 5-142

Find the lengths of the missing sides on the similar shapes at right. What is the scale factor?

Hint 1:

Similar shapes have corresponding sides with equal ratios to each other.

Help:

To find each unknown side, use the ratio between two known corresponding sides.

More Help 1:

For example, the ratio of the $15$ mm side to the $22$ mm side should be equal to the ratio of the $z$ side to the $33$ mm side.

Hint 2:

$\frac{15}{22} = \frac{z}{33}$
Now solve for $z$ .

Partial Answer:

$z=22.5$ mm
You can now use that to find ratios for the other unknown sides.

More Help 2:

Write two more ratios to solve for side $x$ and side $y$ .

More Help 3:

$\frac{15}{54} = \frac{22.5}{y}$
$15y=(22.5)(54)$

Answer:

$y=81$ mm
Now what does $x$ equal?

A five sided polygon, labeled original, sides labeled, starting at the top, as follows: 15 mm, 22 mm, blank, x, 54 mm.

A larger, five sided polygon, labeled copy, in the same orientation as the smaller, with sides labeled, starting at the top: z, 33 mm, blank, 40 mm, y.