Question

two similar triangles, smaller triangle is 3.25 and 4.23, one of the side of the larger triangle is 13 find the length of the other side (x)

Answer 1

To find the length of the other side \( x \) of the larger triangle, we can use the property of similar triangles, which states that the ratios of the corresponding sides are equal.

Given the smaller triangle has sides 3.25 and 4.23, and one side of the larger triangle is 13, let's denote the corresponding side of the larger triangle as \( x \).

We first find the scale factor between the triangles. We can use the ratio of one corresponding side to find the scale factor:

\[
\text{Scale Factor} = \frac{\text{Side of Larger Triangle}}{\text{Corresponding Side of Smaller Triangle}}
\]

Using 3.25 (the shorter side of the smaller triangle) as the corresponding side:

\[
\text{Scale Factor} = \frac{13}{3.25}
\]

Now, calculate this:

\[
\text{Scale Factor} = \frac{13}{3.25} = 4
\]

Now that we have the scale factor, we can find the corresponding side of the larger triangle that relates to 4.23 from the smaller triangle:

\[
x = 4.23 \times 4
\]

Now, calculate \( x \):

\[
x = 4.23 \times 4 = 16.92
\]

Thus, the length of the other side \( x \) of the larger triangle is \( 16.92 \).