Question : In $\triangle$ABC the height CD intersects AB at D. The mid-points of AB and BC are P and Q, respectively. If AD = 8 cm and CD = 6 cm then the length of PQ is:

Option 1: 3 cm

Option 2: 7 cm

Option 3: 9 cm

Option 4: 5 cm

Question : $\triangle ABC \sim \triangle DEF$ and the perimeters of $\triangle ABC$ and $\triangle DEF$ are 40 cm and 12 cm respectively. If DE = 6 cm then AB is:

Option 1: 12.6 cm

Option 2: 24 cm

Option 3: 20 cm

Option 4: 10 cm

Question : Points $P$ and $Q$ lie on sides $AB$ and $AC$ of triangle $ABC$, respectively, such that segment $PQ$ is parallel to side $BC$. If the ratio of areas of triangle $APQ$ to triangle $ABC$ is 25 : 36, then the ratio of $AP$ to $PB$ is:

Option 1: $5:6$

Option 2: $1:5$

Option 3: $6:5$

Option 4: $5:1$

Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.

Option 1: 18 cm

Option 2: 16 cm

Option 3: 20 cm

Option 4: 22 cm

Question : The midpoints of AB and AC of a $\triangle ABC$ are X and Y, respectively. If BC + XY = 18 cm, then the value of BC – XY is:

Option 1: 12 cm

Option 2: 6 cm

Option 3: 8 cm

Option 4: 4 cm