The ratio of area of a rectangle to a square is 7 : 6 and the perimeter of the square is 96 cm. If the ratio of length to breadth of the rectangle is 21 : 8, then find the perimeter of the rectangle (in cm)?

Explanation

Information Given: Ratio of area of rectangle to square = 7 : 6 Perimeter of square = 96 cm Ratio of length to breadth of rectangle = 21 : 8 Asked: Perimeter of rectangle Concept/Formula Used: Perimeter of square = 4 × side Area of square = side × side Area of rectangle = length × breadth Perimeter of rectangle = 2 × (length + breadth) Explanation: Side of square = Perimeter/4 = 96/4 = 24 cm Area of square = 24 × 24 = 576 sq cm Let area of rectangle = A Given ratio of areas is 7 : 6, so: A / 576 = 7 / 6 A = (7 / 6) × 576 = 672 sq cm Ratio of length to breadth of rectangle = 21 : 8 Let length = 21k and breadth = 8k Area of rectangle = length × breadth = 21k × 8k = 168k² 168k² = 672 k² = 672/168 = 4 k=2 Length = 21 × 2 = 42 cm, Breadth = 8 × 2 = 16 cm Perimeter of rectangle = 2 × (42 + 16) = 2 × 58 = 116 cm Short Trick: Side of square = 96 / 4 = 24 Area square = 24 × 24 = 576 Area rectangle = (7 / 6) × 576 = 672 Length : breadth = 21 : 8 → Area = 168k² 168k² = 672 → k = 2 Perimeter rectangle = 2 × (42 + 16) = 116 cm