Question

ABCD is a rectangle of dimensions 80 cm × 60 cm. Another rectangle PQRS is drawn inside ABCD leaving space of equal width x cm along the edges of ABCD. If area PQRS is half of the area ABCD, then find the value of x.

Answer 1

PQ = (80 – 2x) cm

QR = (60 – 2x) cm

Now, Area of PQRS = `1/2` × Area of ABCD

⇒ `(80 - 2x)(60 - 2x) = 1/2 xx 80 xx 60`

⇒ 2(40 – x)2(30 – x) = 40 × 60

⇒ x² – 70x + 1200 = 600

⇒ x² – 70x + 600 = 0

⇒ x² – 10x – 60x + 600 = 0

⇒ x = 10, 60

But x ≠ 60, Hence, x = 10 m.