Question

The length of a rectangle is 3 cm more than twice the width. The area is 1890 cm^2. Find the length and the width of the rectangle.

Answer 1

Answer:

Width = 30 cm; length = 63 cm

Step-by-step explanation:

Represent the width by w and the length by 2w+3 (all measured in cm).

The area of this rectangle is A = (length)(width) = (2w+3)(w) = 1890 (all in cm^2).

Simplifying this expression, we get 2w^2 + 3w = 1890; putting this into the standard form of a quadratic, we get 2w^2 + 3w - 1890 = 0

The coefficients of this quadratic are a = 2, b = 3 and c = -1890.

The roots are then:

        -3 ± √ (9 - 4(2)(-1890) )

        ---------------------------------

                        4, or

         -3 ± √15129       -3 ± 123

  w = ------------------- = ---------------

                4                       4

We find and keep only the + w value, since w is a width.

         120

w = ---------------- = 30 units.

If the width is 30 units, then the length is 2w+3 cm, or 63 cm.

Note that (30)(63) cm^2 = 1890 cm^2, as specified.

              4