Given:
[tex]\Delta STR\cong \Delta LMN[/tex]
[tex]SR=7b+8[/tex]
[tex]LN=11b-12[/tex]
To find:
The value of b and SR.
Solution:
We have,
[tex]\Delta STR\cong \Delta LMN[/tex] (Given)
[tex]ST\cong LN[/tex] (CPCTC)
[tex]ST=LN[/tex]
Substituting the given values, we get
[tex]7b+8=11b-12[/tex]
[tex]7b-11b=-8-12[/tex]
[tex]-4b=-20[/tex]
Divide both sides by -4.
[tex]\dfrac{-4b}{-4}=\dfrac{-20}{-4}[/tex]
[tex]b=5[/tex]
Now,
[tex]SR=7b+8[/tex]
[tex]SR=7(5)+8[/tex]
[tex]SR=35+8[/tex]
[tex]SR=43[/tex]
Therefore, the value of b is 5 and the measure of SR is 43 units.
