Answer:
RS = 38
Explanation:
Given ∆XYZ ~ ∆RST with XY=5x-3, XZ=60, RS=3x+2, RT=40, you want the length of RS.
Similar triangles
Corresponding sides of similar triangles have the same ratios:
XY/XZ = RS/RT
(5x -3)/60 = (3x +2)/40 . . . substitute given lengths
2(5x -3) = 3(3x +2) . . . . . . . multiply by 120
10x -6 = 9x +6 . . . . . . . . . . . eliminate parentheses
x = 12 . . . . . . . . . . . . . . . add 6-9x to both sides
Side RS
Using this value of x we can find RS:
RS = 3x +2
RS = 3(12) +2
RS = 38
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Additional comment
The value of XY is 5(12)-3 = 57, and the above ratio equation becomes ...
57/60 = 38/40 . . . . . both ratios reduce to 19/20.