SOLUTION: The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture the illustration is

Algebra.Com
Question 214239This question is from textbook
: The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture
the illustration is a square inside a squre. the frame
with a width of 12 inches and a hight of 10 inches
I hope thats enough info 2 help me

This question is from textbook

Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture
the illustration is a square inside a squre. the frame
with a width of 12 inches and a hight of 10 inches
.
Draw a diagram of the problem, label all the information given it'll help you see the solution.
.
Let w = width of frame
then measure of picture is:
12-2w = width of picture
10-2w = length of picture
.
Area of picture is (length times width):
(12-2w)(10-2w)
.
Area of frame:
2(10w) + 2w(12-2w)
.
Setting them equal":
(12-2w)(10-2w) = 2(10w) + 2w(12-2w)
120-24w-20w+4w^2 = 20w + 24w - 4w^2
120-44w+4w^2 = 44w - 4w^2
8w^2+120-44w = 44w
8w^2-88w+120 = 0
w^2-11w+15 = 0
Using the quadratic equation we get two solutions:
w={9.40512483795333, 1.59487516204667}
It wouldn't make sense to have a 9+ inch width frame so the answer MUST be:
w = 1.595 inches (width of frame)
.
Details of the quadratic equation to follow:
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=61 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 9.40512483795333, 1.59487516204667. Here's your graph:
RELATED QUESTIONS

A picture 18 cm by 15 cm, has a uniform frame around it. If the area of the frame is 234... (answered by lwsshak3)
A picture is 5 inches by 7 inches. There is a frame around the picture that is of uniform (answered by josgarithmetic)
A wooden frame surrounds a 5 inch by 7 inch photograph. The frame is the same width all... (answered by josmiceli)
The width of a rectanglar picture frame is 5in less its length. The area equal 150sq in.... (answered by mananth)
A picture measuring 40cm by 60cm is surrounded by a frame of uniform width. If the... (answered by checkley71)
A Frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by... (answered by Alan3354)
a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm.... (answered by nerdybill)
The area of a rectangular picture frame is 112cm squared. If the frame is 6 centimeters... (answered by ewatrrr)
A picture is 5cm longer than it is wide. It is in a frame that has a width of 4cm. The... (answered by stanbon,StarPhone)