In a triangle PQR, the length of the side QR is less than twice the length of the side PQ by 3 cm. Length of the side PR exceeds length of the side PQ by 12 cm. If the perimeter of the triangle is 57 cm, then 50% of the length of the smallest side of ΔPQR is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 6 cm.
Let PQ = x cm
So,
QR = 2 × PQ - 3
⇒ QR = (2x - 3) cm
Again
PR = PQ + 12
⇒ PR = (x + 12) cm
Now, according to the question,
(2x - 3) + x + (x + 12) = 57
⇒ 4x + 9 = 57
⇒ 4x = 48
⇒ x = 48/4 = 12 cm
So, PQ = 12 cm
QR = 2 × 12 - 3 = 21 cm
PR = 12 + 12 = 24 cm
PQ is the smallest side of the triangle PQR
50% of PQ = 12 × 50% = 6 cm