SOLUTION: a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm. how far is it from the edge of the picture of the frame if its distance is uniform around the

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Question 901966: a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm. how far is it from the edge of the picture of the frame if its distance is uniform around the picture
Answer by nerdybill(7384) (Show Source):
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a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm. how far is it from the edge of the picture of the frame if its distance is uniform around the picture
.
Let x = width (cm) of frame
then
(35-2x)(25-2x) =375
875 - 70x - 50x + 4x^2 = 375
875 - 120x + 4x^2 = 375
4x^2 - 120x + 875 = 375
4x^2 - 120x + 575 = 0
.
applying the quadratic formula we get:
x = {24, 6}
throw out the 24 (extraneous) leaving
x = 6 cm
.
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=5200 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 24.01387818866, 5.98612181134003. Here's your graph: