Question

The two triangles below are similar (but not drawn to scale). Find the value of x . Round answer to the nearest tenth.
triangle one is 39.5inc and 14.3inc. triangle two is x and 22.6 inc

Answer 1

Since the triangles are similar, the ratios of their corresponding sides are equal. We can set up a proportion using the sides of the triangles.

Let the sides of Triangle One be \( a = 39.5 \) inches and \( b = 14.3 \) inches, and the sides of Triangle Two be \( c = x \) inches and \( d = 22.6 \) inches.

From the property of similar triangles, we can write the proportion:

\[
\frac{39.5}{x} = \frac{14.3}{22.6}
\]

Now, we can solve for \( x \).

First, cross-multiply:

\[
39.5 \cdot 22.6 = 14.3 \cdot x
\]

Calculating \( 39.5 \cdot 22.6 \):

\[
39.5 \cdot 22.6 = 892.7
\]

Thus, we have:

\[
892.7 = 14.3 \cdot x
\]

Now divide both sides by 14.3 to solve for \( x \):

\[
x = \frac{892.7}{14.3} \approx 62.3
\]

Rounding to the nearest tenth, the value of \( x \) is:

\[
\boxed{62.3}
\]