Question

In ΔPQR, QR = 10, RP =11 and PQ = 12. D is the midpoint of PR, DE is drawn parallel to PQ meeting QR in E. EF is drawn parallel to RP meeting PQ in F. What is the length of DF?

(a) \(\frac{11}{2}\) 

(b) 6 

(c) \(\frac{33}{4}\)

(d) 5

Answer 1

(d) 5

D is the mid-point of PR and DE || PQ.

∴ E is the mid-point of QR (Mid-point Theorem) 

∵ E is the mid-point of QR and EF || PR, 

F is the mid-point of PQ (Mid-point Theorem)

∴ DF = \(\frac{1}{2}\times{QR}=\frac12\times10=5.\)