Questions: If triangle NML is similar to triangle SRL, find the value of x.

Transcript text: If $\triangle N M L \sim \triangle S R L$ find the value of $x$.

Solution

Step 1: Set up the proportion

Since $\triangle NML \sim \triangle SRL$, the corresponding sides are proportional. We can set up a proportion using the given side lengths:

$\frac{ML}{LR} = \frac{NL}{LS}$

Step 2: Substitute the given values

Substitute the given values into the proportion:

$\frac{28}{24} = \frac{3x - 1}{x + 7}$

Step 3: Simplify and solve for x

Simplify the fraction and cross-multiply:

$\frac{7}{6} = \frac{3x - 1}{x + 7}$

$7(x + 7) = 6(3x - 1)$

$7x + 49 = 18x - 6$

$49 + 6 = 18x - 7x$

$55 = 11x$

$x = \frac{55}{11}$

$x = 5$

\$\boxed{x = 5}\$

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