In a ΔPQR, PQ = PR and the perimeter of ΔPQR is 8(2 + \(\sqrt {2}\)) cm. If the length of QR is \(\sqrt {2}\) times the length of PQ, then find the area of ΔPQR (in cm2) ?
Answer & explanation
Correct answer: option 2
ATQ,
PQ = PR = 1 and QR = \(\sqrt {2}\)
Perimeter of ΔPQR = (2 + \(\sqrt {2}\)) unit
⇒ (2 + \(\sqrt {2}\)) unit = 8 (2 + \(\sqrt {2}\)) cm
⇒ 1 unit = 8 cm
⇒ Area of ΔPQR = \(\frac{1}{2}\) × PR × PQ = \(\frac{1}{2}\) × 8 × 8 = 32 cm2