Question

Let Upper Delta DOT tilde Upper Delta PANΔDOT~ΔPAN. Find the missing side x.

D
T
O
P
N
A
21 m
x
14 m
54 m
Question content area bottom
Part 1
xequals=enter your response here m ​(Type an integer or a​ fraction.)

Answer 1

To solve for the missing side \( x \) in the triangle \( \Delta PAN \) given that it is similar to another triangle \( \Delta \DOT P \), we can use the properties of similar triangles. The ratios of corresponding sides of similar triangles are equal.

Given the sides of triangle \( \Delta PAN \):
- Side \( PA = 21 \, m \)
- Side \( AN = 14 \, m \)
- Side \( PN = 54 \, m \)
- Side \( DT = x \, m \)

Since the triangles are similar, we can set up the following proportion using corresponding sides:

\[
\frac{PA}{DT} = \frac{AN}{TO} = \frac{PN}{OT}
\]

If we let \( TO \) represent the side corresponding to \( x \), we will use just two sides for this calculation.

Set up the proportion using \( PA \) and \( DT \):

\[
\frac{21}{x} = \frac{14}{54}
\]

Now we can solve for \( x \). First, cross multiply:

\[
21 \times 54 = 14 \times x
\]

Calculating \( 21 \times 54 \):

\[
21 \times 54 = 1134
\]

Now the equation is:

\[
1134 = 14x
\]

Next, divide both sides by 14 to solve for \( x \):

\[
x = \frac{1134}{14} = 81
\]

Thus, the value of \( x \) is:

\[
x = 81 \, m
\]

So the missing side \( x \) is \( 81 \, m \).