Question

ABCD and PQRS are rectangles. O is the centre of both rectangles. AC is a straight line passing through P, Q and R. BD is a straight line passing through Q, R and S. PQ=8cm and QR=2cm. The perimeter of rectangle ABCD is 60cm. Work out the length of AB and the length of BC.

Answer 1

Answer: See below

Explanation:

ΔPQR ≈ ΔABC because PR & AC are same line

So PQ ║ AB & QR ║ BC

In equation form: PQ / AB = QR / BC

8/AB = 2/BC

AB = 4BC

Perimeter of ABCD rectangle = 2(AB + BC)

= 2(4BC + BC)

= 10BC

Perimeter of the rectangle = 60 cm

In equation form: 10BC = 60

BC = 6 cm

AB = 4BC = 24 cm

Length of AB = 24 cm & length of BC = 6 cm