Question

6-90. for the pairs of similar shapes below, find the lengths of the missing sides. be sure to show your calculation. you can choose which shape is “new” and which is “original” in each pair. assume the shapes are drawn to scale. the shapes in part (b) are parallelograms and the shapes in part (d) are trapezoids.
a.
b.
c.
d.

Explanation:

Part a

Step1: Find similarity ratio

The ratio of sides is $\frac{33}{11}=3$

Step2: Solve for $x$

$x = \frac{39}{3}$
$x=13$ cm

Step3: Solve for $y$

$y = 9\times3$
$y=27$ cm

Part b

Step1: Find similarity ratio

The ratio of sides is $\frac{24}{6}=4$

Step2: Solve for $x$

$x = 9\times4$
$x=36$ in

Step3: Solve for $y$

$y = \frac{24}{4}$
$y=6$ in

Part c

Step1: Find similarity ratio

The ratio of sides is $\frac{35}{10}=3.5$

Step2: Solve for $x$

$x = \frac{17.5}{3.5}$
$x=5$ m

Step3: Solve for $y$

$y = \frac{25}{3.5}=\frac{50}{7}\approx7.14$ m

Step4: Solve for $z$

$z = 8\times3.5$
$z=28$ m

Part d

Step1: Find similarity ratio

The ratio of sides is $\frac{6}{4}=1.5$

Step2: Solve for $x$

$x = 6\times1.5$
$x=9$ ft

Step3: Solve for $y$

$y = \frac{12}{1.5}$
$y=8$ ft

Step4: Solve for $z$

$z = \frac{5.7}{1.5}$
$z=3.8$ ft

Answer:

a. $x=13$ cm, $y=27$ cm
b. $x=36$ in, $y=6$ in
c. $x=5$ m, $y=\frac{50}{7}\approx7.14$ m, $z=28$ m
d. $x=9$ ft, $y=8$ ft, $z=3.8$ ft