CPM Homework Help : CC3MN Problem 8-12

Find the lengths of the missing sides on the similar shapes at right.

Two 5 sided enclosed figures. The larger figure goes up 54 mm, then right 15 mm, then down 22 mm, then diagonally right and down, an unknown length, then back to start to enclose the figure a distance of x. The smaller figure goes up y distance, right z distance, down 33 mm, diagonally right and down, an unknown length, and back to start 40 mm to enclose the figure.

Hint:

Similar shapes have sides with equal ratios to each other. To find each unknown side, compare its ratio to a known side.

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.

$\frac{15}{22}=\frac{\it z}{33}$

$z = 22.5 \text{ mm}$

More Help 2:

You can now use the value of $z$ to find ratios for the other unknown sides. Write two more ratios to solve for side $x$ and side $y$ .

Step 1:

$\frac{15}{54}=\frac{22.5}{\it y}$

Step 2:

$15y = \left(22.5\right) \left(54\right)$

Answer:

$y = 81 \text{ mm}$
What does $x$ equal?