Question

In the given figure AB||CD. Find x + y if all measurements are indicated in centimeter.

• A. 4.5 cm
• B. 7.5 cm
• C. 6.5 cm
• D. 2.75 cm

Answer 1

The correct option is B 7.5 cm

Given AB||CD then alternate angle

$\angle AZB=\angle CZD$

$\angle ABZ=\angle CDZ$

$\angle BAZ=\angle ZCD$

$\Delta ABZ\sim \Delta ZDC$

$\therefore \frac{AB}{DC}=\frac{AZ}{ZD}=\frac{BZ}{ZC}$

Given $AB=5cm,BZ=y,ZC=1.8CD=3,ZD=2.8$ and $ZC=1.8$

$\Rightarrow \frac{5}{3}=\frac{x}{2.7}=\frac{y}{1.8}$

$\Rightarrow x=\frac{5}{3}\times 2.7=4.5$ cm

$\Rightarrow y=\frac{5}{3}\times 1.8=3$cm

$\therefore x+y=4.5+3=7.5$ cm