Answer:
In order to determine the dimensions (length and width) of the rectangle, we first have to resolve the area; x²-10x+21, which is a quadratic equation. And by doing so, we'll have:
x² - 10x + 21 = (x - 7)(x - 3)
Given that x = 8cm, the length, l = {8 - 7} = 1cm
and the width, w = {8 - 3} = 5cm
Step-by-step explanation:
To resolve the area: x² - 10x + 21, we have that:
[tex] {x}^{2} - 10x + 21 \\ = {x}^{2} - 7x - 3x + 21 \\ = x(x - 7) - 3(x \: - 7) \\ = (x - 7)(x - 3).[/tex]
From the above solution, to find the dimensions of the rectangle, we will substitute the given value of x (x = 8) into the solution set (x - 7)(x - 3).
[tex]length = (x - 7) \\ = 8 - 7 \\ = 1cm.[/tex]
Also, to find the width, we have:
[tex]width = (x - 3) \\ = 8 - 3 \\ = 5cm.[/tex]
Therefore, the dimensions of the rectangle are length = 1cm and width = 5cm.
