Question

Find all possible values of x in the similar triangles pqr stu

Answer 1

If triangles PQR and STU are similar then PQ corresponds to ST and PR corresponds to SU. Therefore, PQ/ST=PR/SU
Considering that, PQ= 7-x, ST= 13-x, PR= x²+5 and SU= x² +20
therefore, (7-x)/(13-x)= (x²+5)/(x²+20) 
               cross multiplying,
         7x² +140-x³+20x =13x²+65-x³-5x
combining the like terms,
          6x² +15x -75=0
          solving for x,
    x = 5/2 or -5