Question

In the given figure, $\frac{DE}{BC}$, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm. Select the statements that hold true.

• A. ME = 3.75 cm, DM = 15 cm
• B. ME = 3.75 cm, DM = 12 cm
• C. ME = 4 cm, DM = 10 cm
• D. ME = 3.25 cm, DM = 15 cm

Answer 1

The correct option is A

ME = 3.75 cm, DM = 15 cm

In the given figure,

$DE\parallel BC$

AE = 15 cm, EC = 9 cm

NC = 6 cm and BN = 24 cm

In $\Delta ABC$

$DE\parallel BC$

$\therefore$ Pairs of similar triangles are

(a) $\Delta ADE\sim \Delta ABC$

(b) $\Delta ADM\sim \Delta ABN$

(c) $\Delta AME\sim \Delta ANC$

In $\Delta AME\sim \Delta ANC$ (corresponding sides are proportional)

$\Rightarrow \frac{15}{15+9}=\frac{ME}{6}=\frac{DM}{24}$

$\Rightarrow ME=\frac{15\times 6}{24}=\frac{15}{4}=3.75\text{cm}$

Similarly

In $\Delta ADE\sim \Delta ABC$ (corresponding sides are proportional)

$\Rightarrow \frac{15}{15+9}=\frac{DM+ME}{24+6}$

$\Rightarrow \frac{15}{24}=\frac{DM+3.75}{30}$

$DM+3.75=18.75$

$DM=15cm$