Qtn 20: a) Find the dimensions of a rectangle. b) Determine the amount received by each Partner that year.

Here's the solution to Qtn 20: a) Find the dimensions of a rectangle. Step 1: Define variables for the dimensions. Let w be the width of the rectangular plot in feet. Let l be the length of the rectangular plot in feet. Step 2: Set up equations based on the problem statement. The length exceeds the width by 7 ft: l = w + 7 The area of the plot is 60 sq. ft: l × w = 60 Step 3: Substitute the expression for l into the area equation. (w+7)w = 60 w^2 + 7w = 60 Rearrange into a standard quadratic equation: w^2 + 7w - 60 = 0 Step 4: Solve the quadratic equation for w. We can factor the quadratic equation. We need two numbers that multiply to -60 and add to 7. These numbers are 12 and -5. (w+12)(w-5) = 0 This gives two possible solutions for w: w+12 = 0 w = -12 w-5 = 0 w = 5 Since width cannot be negative, we take w=5 ft. Step 5: Calculate the length l. Using l = w + 7: l = 5 + 7 l = 12 ft The dimensions of the rectangle are 12 ft by 5 ft. The final answer for part (a) is Length = 12 ft, Width = 5 ft. b) Determine the amount received by each Partner that year. Step 1: Calculate the total capital contribution. Wabusi: 300,000 Aisha: 500,000 Wekesa: 700,000 Total Capital (C) = 300,000 + 500,000 + 700,000 = 1,500,000 Step 2: Calculate the total profit realized. The profit was one and (1)/(4) times the capital: Profit (P) = 1(1)/(4) × C = (5)/(4) × 1,500,000 P = 5 × 375,000 = 1,875,000 Step 3: Calculate the amount ploughed back into the business. (1)/(3) of the profit was ploughed back: Ploughed back amount = (1)/(3) × 1,875,000 = 625,000 Step 4: Calculate the remainder after ploughing back. Remainder_1 = P - Ploughed back amount = 1,875,000 - 625,000 = 1,250,000 Step 5: Calculate the amount kept for emergency. (1)/(5) of the remainder was kept for emergency: Emergency fund = (1)/(5) × 1,250,000 = 250,000 Step 6: Calculate the amount to be shared among partners. Amount to be shared (S) = Remainder_1 - Emergency fund = 1,250,000 - 250,000 = 1,000,000 Step 7: Determine the ratio of capital contributions. Wabusi : Aisha : Wekesa = 300,000 : 500,000 : 700,000 Simplify the ratio by dividing by 100,000: Ratio = 3 : 5 : 7 Total parts in the ratio = 3 + 5 + 7 = 15 Step 8: Calculate each partner's share of the amount to be shared. Wabusi's share = (3)/(15) × 1,000,000 = (1)/(5) × 1,000,000 = 200,000 Aisha's share = (5)/(15) × 1,000,000 = (1)/(3) × 1,000,000 = (1,000,000)/(3) ≈ 333,333.33 Wekesa's share = (7)/(15) × 1,000,000 = (7,000,000)/(15) ≈ 466,666.67 The amounts received by each partner are: • Wabusi: 200,000 • Aisha: 333,333.33 (rounded to two decimal places) • Wekesa: 466,666.67 (rounded to two decimal places) That's 2 down. 3 left today — send the next one.