Question

1. each pair of polygons below is similar. review what you have learned about similarity as you solve for x. a. 2 6 4 x b. x - 5 4 3 6 c. x 3 21 perimeter = 60

Explanation:

Step1: Set up proportion for similar - polygons

For similar polygons, the ratios of corresponding sides are equal.

a.

The ratio of the short - sides of the two rectangles is the same as the ratio of the long - sides. So, $\frac{2}{4}=\frac{6}{x}$.

Step2: Cross - multiply

Cross - multiplying gives $2x = 4\times6$.

Step3: Solve for $x$

$2x=24$, then $x = 12$.

b.

The ratio of the corresponding vertical sides is $\frac{x - 5}{3}=\frac{4}{6}$.

Step1: Cross - multiply

Cross - multiplying gives $6(x - 5)=3\times4$.

Step2: Expand and solve

$6x-30 = 12$, then $6x=12 + 30=42$, and $x = 7$.

c.

First, find the other side of the larger rectangle. Let the other side of the larger rectangle be $y$. The perimeter of a rectangle is $P = 2(l + w)$. Given $P = 60$ and $l = 21$, then $60=2(21 + y)$.

Step1: Solve for $y$

$60=42 + 2y$, $2y=60 - 42 = 18$, $y = 9$.
The ratio of the short - sides of the two rectangles is the same as the ratio of the long - sides. So, $\frac{3}{9}=\frac{x}{21}$.

Step2: Cross - multiply

Cross - multiplying gives $9x=3\times21$.

Step3: Solve for $x$

$9x = 63$, $x = 7$.

Answer:

a. $x = 12$
b. $x = 7$
c. $x = 7$