Question

In the figure, if $AB\parallel EF\parallel CD$, such that $AB=7.5cm,EG=2.5cm,GC=5cm$ and $DC=9cm$ then $AC$=

• A. $9cm$
• B. $12.5cm$
• C. $6cm$
• D. $8cm$

Answer 1

The correct option is A $9cm$

Since $AB\parallel EF\parallel CD$, and AB=7.5cm, EG=2.5cm, GC=5cm, DC=9cm, and we have to find the value of AC.

$\frac{AB}{EF}=\frac{EC}{AC}$

$\frac{7.5}{EF}=\frac{7.5}{AC}$

$\frac{7.5}{EF}=\frac{7.5}{7.5+AE}$

$⟹AE+7.5=EF$-----(1)

Now consider triangles EFC and CDF,

$\frac{FC}{EF}=\frac{FC}{CD}$

We get $EF=CD$

So, putting thiss value in (1), we get

From above, $AE+7.5=9$

$AE=1.5$

Now, as we know, $AC=AE+EG+GC$

$AC=1.5+2.5+5$

Therefore $AC=9cm$

(Answer)