Answer:
x = 12
Explanation:
Given ∆ABC ~ ∆RTS, AC = 25, BC = 40, RS = (x+18), TS = 48, you want the value of x.
Similar triangles
In similar triangles, corresponding sides are proportional:
RS/AC = TS/BC
(x+18)/25 = 48/40
x +18 = 25(6/5) . . . . . . . multiply by 25, simplify the fraction
x = 30 -18 . . . . . . . . subtract 18
x = 12
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Additional comment
Then RT/AB = 36/(2·12 +6) = 36/30 = 6/5, as required for similarity.