An illustration shows a larger triangle upper N upper T upper E and a smaller triangle upper K upper L upper A, with labeled sides. On the first triangle, side upper E upper N is the base labeled as 63, side upper T upper E is on the right labeled as 99, and side upper N upper T is on the left and is not labeled. On the second triangle, side upper A upper K is the base that is labeled as 7, side upper L upper A is on the right labeled as x, and side upper K upper L is on the left and is not labeled.

Question

Triangle NTE is similar to triangle KLA. If TE = 99, EN = 63, and AK = 7, what is the length of LA?

Answer 1

Since triangles \( NTE \) and \( KLA \) are similar, the ratios of the corresponding sides are equal. We can set up the ratio using the given side lengths:

\[ \frac{EN}{AK} = \frac{TE}{LA} \]

The values we have are:

• \( EN = 63 \)
• \( AK = 7 \)
• \( TE = 99 \)

Let \( LA \) be the unknown side length we need to find. Plugging in the known values, we have:

\[ \frac{63}{7} = \frac{99}{LA} \]

Now, we can simplify the left side:

\[ \frac{63}{7} = 9 \]

So the equation becomes:

\[ 9 = \frac{99}{LA} \]

Now, we can cross-multiply to solve for \( LA \):

\[ 9 \cdot LA = 99 \]

Dividing both sides by 9 gives:

\[ LA = \frac{99}{9} = 11 \]

Thus, the length of \( LA \) is \( \boxed{11} \).