Question

In figure below (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).
(i)
(ii)

Answer 1

(i)
Let EC = x cm.
Given DE || BC.
By the basic proportionality theorem:
\(\frac{AD}{DB}=\frac{AE}{EC}\)
\(\frac{1.5}{3}=\frac{1}{x}\)
\(x=3\times \frac{1}{1.5}\)
x=2.
Therefore, EC = 2 cm.

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(ii)
Let AD = x cm.
Given DE || BC.
By the basic proportionality theorem:
\(\frac{AD}{DB}=\frac{AE}{EC}\)
\(\frac{x}{7.2}=\frac{1.8}{5.4}\)
x=\(\frac{1.8\times 7.2}{5.4}\)
x=2.4.
Therefore, AD = 2.4 cm.