In the given figure, in triangle STU, ST = 8 cm, TU = 9cm, and SU = 12 cm. QU = 24 cm, SR = 32 cm and PT = 27 cm. What is the ratio of the area of triangle PTR and the area of triangle PQU?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 9 : 4.
Let Area of ΔPQU = A1
Let Area of ΔPTR = A2
Let Area of ΔSUT = A
⇒ A = 1/2 × SU × UT × sinα
⇒ A = 1/2 × 12 × 9 × sinα
⇒ A1 = 1/2 × PU × QU × sin(π - α)
⇒ A1 = 1/2 × 18 × 24 × sinα
⇒ A1/A = (18 × 24)/(12 × 9) = 4/1
⇒ A2 = 1/2 × PT × TR × Sin(180 - β)
⇒ A2 = 1/2 × 9 × 8 × Sin β
⇒ A2/A = (27 × 24)/(9 × 8) = 9/1
So,
⇒ A2/A2 = 9/4 = 9 : 4