SOLUTION: 52. A rectangular painting has dimensions x and x + 10. The painting is in a frame 2 in. wide. The total area of the picture and the frame is 900 in.

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Question 575668: 52. A rectangular painting has dimensions x and x + 10. The painting is in a
frame 2 in. wide. The total area of the picture and the frame is 900 in.
Answer by JBarnum(2146)   (Show Source): You can put this solution on YOUR website!

how did i get this equation?
the frame is 2 inches thick so theres 2 inches on left side of the length and 2 inches on the right side so thats 4 more inches than the lenth of the picture
same goes for the width 2 in on top 2 inches on bottom makes 4 more inches added to width
length times width equals area




back to the equation
FOIL (First Outer Inner Last)
F
O
I
L
add like terms
subtract 900 from both sides
use quadratic formula to solve
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=3700 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 21.4138126514911, -39.4138126514911. Here's your graph:
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