Question : In a triangle ${ABC}, {AB}={AC}$ and the perimeter of $\triangle {ABC}$ is $8(2+\sqrt{2}) $ cm. If the length of ${BC}$ is $\sqrt{2}$ times the length of ${AB}$, then find the area of $\triangle {ABC}$.

Option 1: $32 \ cm^2$

Option 2: $28 \ cm^2$

Option 3: $16 \ cm^2$

Option 4: $36 \ cm^2$

Question : Triangle ABC and DEF are similar. If AB = 92 cm, BC = 48 cm, AC =120 cm, and the length of the smallest side of triangle DEF is 200 cm, then find the length of the longest side of triangle DEF.

Option 1: 400 cm

Option 2: 225 cm

Option 3: 350 cm

Option 4: 500 cm

Question : In $\triangle {ABC} $, AB = 48 cm, BC = 55 cm and AC = 73 cm. If O is the centroid of the triangle, then the length (in cm) of BO (correct to one decimal place) is:

Option 1: 25.6

Option 2: 24.3

Option 3: 20.4

Option 4: 18.3

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 : The mid-points of AB and AC of the $\triangle$ABC are P and Q, respectively. If PQ = 6 cm, then the side BC is:

Option 1: 10 cm

Option 2: 12 cm

Option 3: 8 cm

Option 4: 14 cm