Question

triangle length: 11.4 in
triangle base: 18 in

triangle length: x
triangle base: 23.4 in

what is the length of x in decimal form to the nearest hundredth?

Answer 1

To find the length \( x \) of the second triangle, we can use the property of similar triangles, since both triangles share the same angles and have proportional sides.

The ratio of the corresponding sides can be set up as follows:

\[
\frac{\text{length of triangle 1}}{\text{base of triangle 1}} = \frac{\text{length of triangle 2}}{\text{base of triangle 2}}
\]

Plugging in the values we have:

\[
\frac{11.4}{18} = \frac{x}{23.4}
\]

Cross-multiplying gives:

\[
11.4 \times 23.4 = 18 \times x
\]

Calculating \( 11.4 \times 23.4 \) first:

\[
11.4 \times 23.4 = 267.96
\]

Thus, we have:

\[
267.96 = 18x
\]

Now, dividing both sides by 18 to solve for \( x \):

\[
x = \frac{267.96}{18}
\]

Calculating \( \frac{267.96}{18} \) gives:

\[
x \approx 14.88
\]

So, the length of \( x \) in decimal form to the nearest hundredth is:

\[
\boxed{14.88}
\]