Question

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

Answer 1

Given:

$\Delta STR\cong \Delta LMN$

$SR=7b+8$

$LN=11b-12$

To find:

The value of b and SR.

Solution:

We have,

$\Delta STR\cong \Delta LMN$                          (Given)

$ST\cong LN$                                  (CPCTC)

$ST=LN$

Substituting the given values, we get

$7b+8=11b-12$

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

$-4b=-20$

Divide both sides by -4.

$\dfrac{-4b}{-4}=\dfrac{-20}{-4}$

$b=5$

Now,

$SR=7b+8$

$SR=7(5)+8$

$SR=35+8$

$SR=43$

Therefore, the value of b is 5 and the measure of SR is 43 units.