Question

A triangle was dilated
11.4 in by 18 in triangle is the original
After dilation it’s x by 23.4
What is the length of a in decimal form to the nearest hundredth?

Answer 1

To solve the problem, we first need to determine the scale factor of the dilation based on the information provided.

1. **Original dimensions of the triangle:**
- The original triangle has one side measuring 18 inches (let's call this base) and the height measuring 11.4 inches.

2. **New dimensions of the triangle after dilation:**
- One side after dilation measures 23.4 inches.

We'll find the scale factor of the dilation by comparing the sides of the original triangle to the sides of the dilated triangle.

Assuming that the side of length 18 inches corresponds to 23.4 inches after dilation, we can calculate the scale factor (k) as follows:

\[
k = \frac{\text{New Length}}{\text{Original Length}} = \frac{23.4}{18}
\]

Calculating the above:

\[
k = \frac{23.4}{18} \approx 1.3
\]

Now, we apply this scale factor to the other original side, which is 11.4 inches (to find the new side length corresponding to "a").

The new length \( a \) after dilation would be:

\[
a = \text{Original Length} \times k = 11.4 \times 1.3
\]

Calculating \( a \):

\[
a = 11.4 \times 1.3 = 14.82
\]

Thus, the length \( a \) in decimal form to the nearest hundredth is:

\[
\boxed{14.82}
\]