$$ riangle S T R \cong riangle L M N, S R=7 b+8 $$, and $$ L N=11 b-12 $$. Find $$ b $$ and $$ S R $$. $$ b=5 $$ and $$ S R=43 $$ $$ b=5 $$ and $$ S R=67 $$ $$ b=3 $$ and $$ S R=43 $$ $$ b=3 $$ and $$ S R=67 $$

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$$ 	riangle S T R \cong 	riangle L M N, S R=7 b+8 $$, and $$ L N=11 b-12 $$. Find $$ b $$ and $$ S R $$. $$ b=5 $$ and $$ S R=43 $$ $$ b=5 $$ and $$ S R=67 $$ $$ b=3 $$ and $$ S R=43 $$ $$ b=3 $$ and $$ S R=67 $$

UpStudy AI · Accepted Answer

Since the triangles $$ \triangle S T R $$ and $$ \triangle L M N $$ are congruent, their corresponding sides are equal. We have the following information:

1. $$ S R = 7b + 8 $$
2. $$ L N = 11b - 12 $$

Since $$ S R $$ corresponds to $$ L N $$, we can set up the equation:

$$
7b + 8 = 11b - 12
$$

Now, let's solve for $$ b $$:

1. Rearranging the equation gives:
   $$
   7b + 8 + 12 = 11b
   $$
   $$
   20 = 11b - 7b
   $$
   $$
   20 = 4b
   $$
   $$
   b = 5
   $$

Now that we have $$ b $$, we can find $$ S R $$:

$$
S R = 7b + 8 = 7(5) + 8 = 35 + 8 = 43
$$

Thus, we have:

- $$ b = 5 $$
- $$ S R = 43 $$

The correct answer is:

$$
\boxed{b=5 \text{ and } S R=43}
$$
$$ b=5 $$ and $$ S R=43 $$

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