Question

△STR≅△LMN, SR=7b+8, and LN=11b−12. Find b and SR

a) b = 3 and SR = 67
b) b = 5 and SR = 43
c) b = 5 and SR = 67
d) b = 3 and SR = 43

Answer 1

To find the variable b and the length of side SR, set the expressions 7b+8 and 11b-12 equal to each other, solve for b, which is 5, and then substitute this into the expression for SR to get the length of 43.

Step-by-step explanation:

The student's question involves determining the value of the variable b and the length of side SR given that triangles △STR and △LMN are congruent with SR and LN as corresponding sides. According to the given information, SR equals 7b+8 and LN equals 11b−12. Since the triangles are congruent, these two expressions must be equal.

To find the value of b, set the expressions equal to each other:

• 7b + 8 = 11b − 12

Now, solve for b:

• 7b + 8 = 11b − 12
• 8 + 12 = 11b − 7b
• 20 = 4b
• b = 5

Substitute b = 5 into the expression for SR to find its length:

• SR = 7(5) + 8
• SR = 35 + 8
• SR = 43

Therefore, the correct answer is (b) b = 5 and SR = 43.