Question 78

In ΔDEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 3:2 and HF is 8 cm, then the length of DF is

Solution

GH is parallel to EF and G divides DE in the ratio 3:2

Let DG = $$3x$$ cm and GE = $$2x$$ cm and HF = 8 cm

=> $$\frac{DG}{GE} = \frac{DH}{HF}$$

=> $$\frac{3x}{2x} = \frac{DH}{8}$$

=> $$DH = \frac{8 \times 3}{2} = 12$$ cm

$$\therefore$$ DF = DH + HF = 12 + 8 = 20 cm

=> Ans - (B)

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