SOLUTION: The length of a rectangle is 4 cm less than half of its breadth. Its area is 448 square centimeters. Find its length.

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Question 350989: The length of a rectangle is 4 cm less than half of its breadth.
Its area is 448 square centimeters.
Find its length.
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 4 cm less than half of its breadth.
Its area is 448 square centimeters.
.
Breadth is the same as width.
.
Let w = width
then
(1/2)w-4 = length
.
w((1/2)w-4) = 448
Multiplying both sides by 2:
w(w-8) = 896
w^2-8w = 896
w^2-8w-896=0
apply quadratic formula we get:
w = {34.2, -26.2}
Throw out the negative solution to give you:
w = 34.2 cm (width)
.
Length:
(1/2)w-4 = (1/2)34.2-4 = 17.1-4 = 13.1 cm (length)
.
Details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3648 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 34.199337741083, -26.199337741083. Here's your graph: