Answer:
[tex] \boxed{Dimensions\: of \: the \: rectangle \: are \: 15 \: and \: 10 units} [/tex]
Step-by-step explanation:
Let the length of rectangle be 'x' units
So, width of rectangle will be = x - 5 units
Area of rectangle = 150 square units
[tex]=> Area \: of \: rectangle = length × breadth \\ \\ = > 150 = x \times (x - 5) \\ \\ = > 150 =( x \times x )- (x \times 5) \\ \\ = > 150 = {x}^{2} - 5x \\ \\ = > 0 = {x}^{2} - 5x - 150 \\ \\ = > {x}^{2} - 5x - 150 = 0 \\ \\ = > {x}^{2} - (15 - 10)x - 150 = 0 \\ \\ = > {x}^{2} - 15x + 10x - 150 = 0 \\ \\ = > x(x - 15) + 10(x - 15) = 0 \\ \\ = > (x - 15)(x + 10) = 0 \\ \\ = > x - 15 = 0 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: x + 10 = 0 \\ \\ = > x = 15 \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: x = - 10[/tex]
Dimension cannot be negative so the value of x is 15
Therefore,
Length of rectangle = 15 units
Width of rectangle = 15 - 5 = 10 units
