math work and I need help

Question

what is the dimensions of a rectangle if it is -7x+8 and -2x? I was wondering if I could get help with this one because I don't understand it

Answer 1

Hi, thank you for your question. Just a quick reminder: Rectangles have 2 different dimensions: length and width. And some few cases, the area of a rectangle is equal to its perimeter.

Assuming that is the case for your given rectangle, we can set up this equation:

L*W = 2(L+W)

with W= -7x+8 and L = -2x

Hence we have, -2x(-7x+8) = 14x² -16

and 2(-7x+8 - 2x) = -18x + 16

By equalizing the equations, we have 14x² -16 = -18x + 16 => 14x² + 2x - 16 = 0 or 7x² + x - 8 = 0

The factors are: (7x+8)(x-1). Therefore the two solutions are x= 1 and x = -8/7.

The verified solutions is x=-8/7 because it gives positive values for the dimensions of the rectangle.

L= -2x = -2(-8/7)= 16/7

W= -7x+8 = -7(-8/7)+8 = 16