The sum of the lengths of two rectangles P and Q is 26
cm. Their breadths are 6 cm and 4 cm respectively. If the ratio of the perimeter of rectangle P to the perimeter of rectangle Q is 7 : 5, find the difference between their perimeters.

ATQ, The breadth of rectangle P is 6 cm. The breadth of rectangle Q is 4 cm. The ratio of the perimeters of rectangle P and rectangle Q is 7 : 5. Let the perimeter of rectangle P be 7x cm. Let the perimeter of rectangle Q be 5x cm. Formula of perimeter of a rectangle = 2 × (length + breadth). For rectangle P: 2 × (length of P + 6) = 7x. So, length of P + 6 = 7x ÷ 2. Length of P = 7x ÷ 2 − 6. For rectangle Q: 2 × (length of Q + 4) = 5x. So, length of Q + 4 = 5x ÷ 2. Length of Q = 5x ÷ 2 − 4. The sum of the lengths of both rectangles is 26 cm. So, 7x ÷ 2 − 6 + 5x ÷ 2 − 4 = 26. Now, 7x ÷ 2 + 5x ÷ 2 − 10 = 26. 12x ÷ 2 − 10 = 26. 6x − 10 = 26. 6x = 26 + 10 = 36. x = 36 ÷ 6 = 6. Perimeter of rectangle P = 7x = 7 × 6 = 42 cm. Perimeter of rectangle Q = 5x = 5 × 6 = 30 cm. Required difference = 42 − 30 = 12 cm.