SOLUTION: a 5 in. by 7 in. photograph is surrounded by a frame of uniform width. The area of the frame equals the area of the photograph. Find the width of the frame

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Question 286261: a 5 in. by 7 in. photograph is surrounded by a frame of uniform width. The area of the frame equals the area of the photograph. Find the width of the frame
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
A of picture = 5*7=35
.
Frame width = x
.
The area of the frame = area of the picture, which means it is 35+35 = 70
.
(2x+5)(2x+7) = 70
4x^2 +14x +10x + 35 = 70
4x^2 +24x + 35 = 70
4x^2 +24x -35 = 0
.
Using the quadratic solver...
.
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=1136 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.21307488658818, -7.21307488658818. Here's your graph:

.
x = 1.2130 (The other root is negative, so it is spurious.)
.
Checking, what is the area of a rectangle defined by the outside of the frame?
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(5+2(1.2130)) * (7 + 2(1.2130)) = (5+2.426)*(7+2.426) = 7.246*9.246 = 69.997,
which is pretty close to 70.
.
Done.
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