Question

In the adjoining figure $AB||CD||EF.$ The measurements are indicated in centimeter. Find the values of $x$ and $yi$ n centimeter.

• A. $x=\frac{1}{4},y=\frac{20}{3}$
• B. $x=\frac{15}{4},y=\frac{1}{4}$
• C. $x=\frac{5}{8},y=\frac{20}{3}$
• D. $x=\frac{15}{4},y=\frac{20}{3}$

Answer 1

The correct option is D $x=\frac{15}{4},y=\frac{20}{3}$

From figure,

$△ACD$ and $△AFE$

$\Rightarrow \frac{CD}{EF}=\frac{AC}{AE}$

$\frac{x}{10}=\frac{AC}{AE}$ ---(i)

In $ABE,AB||CD$

$\frac{CD}{AB}=\frac{DE}{BE}=\frac{CE}{AE}$ ---------( Since $△CDE\sim △ABE$)

$\frac{x}{6}=\frac{y}{y+4}=\frac{CE}{AE}=\frac{AE-AC}{AE}=1-\frac{AC}{AE}$ ---(ii)

From (i) and (ii)

$\frac{x}{6}=1-\frac{AC}{AE}=1-\frac{x}{10}$

$\frac{16x}{60}=1$

$\Rightarrow x=\frac{15}{4}$

$\frac{x}{6}=\frac{y}{y+4}$

$\frac{y}{y+4}=\frac{15}{4\times 6}=\frac{5}{8}$

$\frac{y+4}{y}=\frac{8}{5}$

$\Rightarrow y=\frac{20}{3}$