Answer: Length = 10cm
Width = 6.5cm
Explanation:
Let the width of the rectangle be represented by x.
Therefore, the length of the rectangle will be: = (2 × x) - 3 = 2x - 3
Therefore area of a rectangle = length × width
x(2x - 3) = 65
2x² - 3x = 65
2x² - 3x - 65 = 0
2x² + 10x - 13x - 65 = 0
2x(x + 5) - 13(x + 5) = 0
(2x - 13)(x + 5) = 0
2x - 13 = 0
2x = 13
x = 13/2
x = 6.5
Width = 6.5cm
Length = 2x - 3
= 2(6.5) - 3
= 13 - 3
= 10cm
Therefore, the length of the rectangle is 10cm and the width is 6.5cm.