Question

In the adjoining figure, DE || AB, AD = 7 cm, CD = 5 cm and BC = 18 cm. Find BE and CE.

Answer 1

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that $DE||AB,AD=7$ cm, $CD=5$ cm and $BC=18$ cm.

Using the basic proportionality theorem, we have

$\frac{CD}{CA}=\frac{DE}{AB}=\frac{CE}{CB}$

$\Rightarrow \frac{CD}{CA}=\frac{CE}{CB}$

$\Rightarrow \frac{5}{12}=\frac{CE}{18}$

$\Rightarrow 18\times 5=12CE$

$\Rightarrow 12CE=90$

$\Rightarrow CE=\frac{90}{12}=7.5$

Since $CE=7.5$ cm, therefore,

$CB=CE+EB$

$\Rightarrow 18=7.5+EB$

$\Rightarrow EB=18-7.5=10.5$

Hence, $BE=10.5$ cm and $CE=7.5$ cm.