Width of the rectangle is 2 units
Step-by-step explanation:
- Step 1: Let the width of the rectangle be x. Then the length = 8 + [tex]\frac{x}{2}[/tex]. Find dimensions of the rectangle if its area = 18 sq. units
Area of the rectangle = length × width
18 = x (8 + [tex]\frac{x}{2}[/tex])
36 = x(16 + x) (Cross multiplying 2)
36 = 16x + x²
x² + 16x - 36 = 0
x² + 18x - 2x - 36 = 0 (Using Product Sum rule to factorize)
x(x + 18) - 2(x + 18) = 0
(x + 18)(x - 2) = 0
x = -18, 2 (negative value is neglected)
x = 2 units
