The length of a rectangular table is 22cm longer than its width suppose the given area is 75cm what is the dimension
Answer (1)
Answer:Let's denote the width of the rectangular table as 'w' centimeters. According to the problem, the length of the table is 22 centimeters longer than its width, so the length can be expressed as 'w + 22' centimeters. The area of a rectangle is calculated by multiplying its length by its width, which gives us the equation:w * (w + 22) = 75Expanding this, we get:w^2 + 22w = 75Rearranging to form a quadratic equation:w^2 + 22w - 75 = 0To find the value of 'w', we can use the quadratic formula:w = [-b ± √(b^2 - 4ac)] / 2a,where a = 1, b = 22, and c = -75.Calculating the discriminant:Δ = (22)^2 - 4 * 1 * (-75) = 484 + 300 = 784Since √784 = 28,we have:w = [-22 ± 28] / 2This gives two solutions:1. w = (-22 + 28) / 2 = 6 / 2 = 3 cm,2. w = (-22 - 28) / 2 = -50 / 2 = -25 cm.Since a negative width is not physically meaningful, the valid solution is w = 3 cm.Therefore, the length of the table is:length = w + 22 = 3 + 22 = 25 cm.**Dimensions of the table:** Width = 3 cm and Length = 25 cm.Step-by-step explanation:
