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

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YoungActivist744 YoungActivist744

14-01-2018
Mathematics

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

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jamuuj jamuuj · Answer 1 · 2018-01-20T07:26:41+01:00

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