Asked by Ian
Triangle QRS is formed by connecting the midpoints of the side of triangle NOP. The lengths of the sides of triangle QRS are shown. What is the length of start overline NP? Figures not necessarily drawn to scale.
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GPT-5 mini
AI
I don't see the figure or the numeric side lengths — could you upload the image or tell me the lengths shown on QRS?
In general: the triangle formed by joining the midpoints of the sides of triangle NOP (the medial triangle QRS) is similar to NOP with scale factor 1/2. Each side of QRS is half the length of the side of NOP that it is parallel to. In the usual labeling (Q midpoint of NO, R midpoint of OP, S midpoint of PN), QR ∥ NP and QR = (1/2)·NP, so NP = 2·QR. (Similarly NP corresponds to 2·(the side of QRS parallel to NP).)
So once you give the length of the side of QRS parallel to NP (or tell me which side that is), I can give the numeric value for NP.
In general: the triangle formed by joining the midpoints of the sides of triangle NOP (the medial triangle QRS) is similar to NOP with scale factor 1/2. Each side of QRS is half the length of the side of NOP that it is parallel to. In the usual labeling (Q midpoint of NO, R midpoint of OP, S midpoint of PN), QR ∥ NP and QR = (1/2)·NP, so NP = 2·QR. (Similarly NP corresponds to 2·(the side of QRS parallel to NP).)
So once you give the length of the side of QRS parallel to NP (or tell me which side that is), I can give the numeric value for NP.
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