Question

In the figure $\angle A=\angle CED,CD=8cm,CE=10cm,BE=2cm,AB=9cm,AD=bandDE=a$. The value of $a+b$ is

• A. $13cm$
• B. $15cm$
• C. $12cm$
• D. $9cm$

Answer 1

The correct option is A $13cm$

According to given statements,

$△ACB$ and $△ECD$, are the similar triangles by AA criterion.

Therefore, their sides are in proportion,

So,

$\frac{AC}{EC}=\frac{CB}{CD}=\frac{BA}{DE}$

=> $\frac{8+b}{10}=\frac{12}{8}=\frac{9}{a}$

On solving these , we get,

$b=7$ and $a=6$

Therefore,

$a+b=13$