The length of a rectangle is twice as long as the side of a square. The side of a square is4 cm longer than the width of the samerectangle. If their areas are equal, find theirdimensions.[4 Marks]

The length of a rectangle is twice as long as the side of a square.

1.	The length of a rectangle is twice as long as the side of a square. The side of a square is4 cm longer than the width of the samerectangle. If their areas are equal, find theirdimensions.[4 Marks]
Answer» Length of RECTANGLE = 16 cmWidth of rectangle = 4 cmSide of square = 8 cmStep-by-step explanation:Let the width of the rectangle be X CM.A/q, Side of the square = (x + 4) cmAlso, Length of rectangle = 2(Side of square)On further solving, we get → Length = 2(x + 4)Now,A.T.Q.,Area of square = Area of rectangle→ (Side of square)² = Length of rectangle × Width of rectanglePutting the known values, we get → (x + 4)² = 2(x + 4) × x→ x² + 16 + 8X = 2x(x + 4)→ x² + 16 + 8x = 2x² + 8x→ 2x² - x² + 8x - 8x - 16 = 0→ x² - 16 = 0→ x² = 16→ x = √16→ x = ± 4Dimensions can't be negative.Hence, x = 4 cm________________________• Length of rectangle = 2(x + 4)→ 2(4 + 4)→ 2(8)→ 16 cm_________________________• Width of rectangle = x→ 4 cm_________________________• Side of square = (x + 4)→ (4 + 4)→ 8 cm