I need help with this word problem ASAP

The road width is x = 10 m.

Step-by-step explanation:

A formula for the area of the horizontal rectangle is A1 = (x)(20 m).

A formula for the small rectangle on top of that is A2 = (x)(18 - x).

The total area of the new roadway is 280 m^2.

Summing up A1 and A2 and equating the result to 280 m^2, we get:

20x + 18x - x^2 = 280

Rewriting this in the standard quadratic form:

-x^2 + 38x - 280 = 0

Here the coefficients are a = -1, b = 38 and c = -280.

The discriminant is thus b^2 - 4ac, or:

38^2 - 4(-1)(-280) = 1444 - 4(280) = 324, or 18^2.

Thus, the roots (x-values) are:

      -38 ± 18

      = 28 and 10

            -2

Only the value x = 10 makes sense here, so we omit the other value (28).

The road width is x = 10 m.

x =

180 square centimeters

step-by-step explanation: