Question

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Answer 1

Answer:

The possible length and width are (2x-1) and (11x-2).

Step-by-step explanation:

We are given that,

Area of the rectangular blanket = $22x^{2}-7x-2$.

As, the area of a rectangle = Length × Width.

We need to find the factors of the polynomial $22x^{2}-7x-2$.

The solution of the equation $ax^{2}+bx+c=0$ is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

So, the solution of $22x^{2}-7x-2=0$ is given by,

$x=\frac{7\pm \sqrt{(-7)^2-4\times 22\times (-2)}}{2\times 22}$

i.e. $x=\frac{7\pm \sqrt{49+176}}{44}$

i.e. $x=\frac{7\pm \sqrt{225}}{44}$

i.e. $x=\frac{7\pm 15}{44}$

i.e. $x=\frac{7+15}{44}$ and $x=\frac{7-15}{44}$

i.e. $x=\frac{22}{44}$ and $x=\frac{8}{44}$

i.e. $x=\frac{1}{2}$ and $x=\frac{2}{11}$

Thus, the factors of the corresponding polynomial are (2x-1) and (11x-2).

That is,

Area of a rectangle = $22x^{2}-7x-2$ = (2x-1) × (11x-2).

Hence, the possible length and width are (2x-1) and (11x-2).