Answer:
5x - 9
Step-by-step explanation:
The area of the rectangle is:
[tex]A=35x^2 -53x-18[/tex] (1)
The area of the rectangle is the product of length (L) and width (W):
[tex]A=LW[/tex]
where [tex]L=7x+2[/tex], and the width must be in the form [tex]W=ax+b[/tex].
We need to find the values of a and b. If we calculate the product of L and W, we get:
[tex]A=LW=(7x+2)(ax+b)=7ax^2 + 7bx+2ax+2b = 7ax^2 +(7b+2a)x+2b[/tex]
We know that this equation must be equivalent to (1), so we immediately see that:
- the coefficient of the second order term, [tex]x^2[/tex], must be 35, so
[tex]7a=35\\a=\frac{35}{7}=5[/tex]
- the zero-order term must be equal to -18, so we have
[tex]2b=-18\\b=-\frac{18}{2}=-9[/tex]
- We can verify that using a=5 and b=-9, the coefficient of the first-order term corresponds to -53:
[tex]7b+2a=7(-9)+2\cdot 5=-63+10=-53[/tex]
So, the width is
W = 5x - 9
