Question

Triangle EFG is similar to Triangle QRS. Gary builds the proportion below to solve for the missing side QR.

EF/FG = QS/QR

Explain what mistake Gary made and how you would correct it.

Answer 1

Triangle EFG is similar to Triangle QRS means that corresponding vertices are E and Q, F and R, and G and S.

Lengths of corresponding sides of similar triangles are in proportion so:

EF/QR = FG/RS = EG /QS
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Gary wrote EF/FG = QS/QR.

That is equivalent to the proportion:

EF/QS = FG /QR

Those are not corresponding sides of these two similar triangles.

Gary should have followed the correspondences given by the statement of the similar triangles and written EF/QR = FG/RS.

Answer 2

EF*QR =QS*FG

QR=(QS*FG)/EF

Answer 3

Thanks Directrix but are you sure that is the right answer?:P