Discussion

Explanation:

OA ⊥ PQ, OB ⊥ PR

OP = OQ = OR = 625 cm

In ∆OAQ, OA = 175 cm and OQ = 625 cm ⇒ AQ = 600 cm

Similarly, PA = PB = RB = 600 cm

∆PQR is an isosceles triangle and PQ = PR = 1200 cm

So, PC ⊥ QR

In ∆PBO and ∆PCR,

∠OPB ≅ ∠RPC   … (Common angle)

∠PBO ≅ ∠PCR   … (Right angle)

∆PBO ~ ∆PCR       … (AA test of similarity)

$\therefore \frac{\mathrm{PB}}{\mathrm{PC}}=\frac{\mathrm{BO}}{\mathrm{CR}}=\frac{\mathrm{PO}}{\mathrm{PR}}$

$\therefore \frac{600}{\mathrm{PC}}=\frac{175}{\mathrm{CR}}=\frac{625}{1200}$

∴ PC = 1152 cm and CR = 336 cm

∴ QR = 672 cm

A(△PQR) = $\frac{1}{2}\times 672\times 1152$ = 387072

Hence, option (b).

» Your doubt will be displayed only after approval.