(a)OR(b)

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

from the base of a lamp post at a speed of $\displaystyle 1.2 \mathrm{~m} / \mathrm{s}$. If the lamp is $\displaystyle 3.6$ m above the ground, find the length of her shadow after $\displaystyle 4$ seconds. $\displaystyle \mathrm{BD}=$ speed × time $\displaystyle =1.2 \times 4=4.8 \mathrm{~m}$ $\displaystyle \Delta \mathrm{ABE} \sim \Delta \mathrm{CDE}$ $\displaystyle \Rightarrow \frac{\mathrm{BE}}{\mathrm{DE}}=\frac{\mathrm{AB}}{\mathrm{CD}}$ $\displaystyle \Rightarrow \frac{4.8+\mathrm{DE}}{\mathrm{DE}}=\frac{3.6}{0.9}$ $\displaystyle \Rightarrow \mathrm{DE}=1.6 \mathrm{~m}$ ∴ Shadow of the girl after walking for $\displaystyle 4$ seconds is $\displaystyle 1.6$ m long