Given that sr⊥qt and that sq≅st, find the perimeter of δqst

a. 22
b. 27
c. 30
d. 32

  D. 32

Step-by-step explanation:

SQ = ST means the triangles SRQ and SRT are congruent, so RQ = RT.

  2x +1 = 3x -1

  2 = x . . . . . . . add 1-2x

Then ST = 5(2)+1 = 11, TR = 3(2)-1 = 5 and the two remaining line segments of the perimeter are the same lengths as these. The perimeter is ...

  P = 2(11 +5) = 32 . . . . units

The perimeter of ΔQST is 32 units.