SOLUTION: The length of a picture is 1 inch less than twice its width. The frame around the picture has a uniform width of 2 inches and an area of 96 square inches. What are the dimensions

Algebra.Com
Question 40285: The length of a picture is 1 inch less than twice its width. The frame around the picture has a uniform width of 2 inches and an area of 96 square inches. What are the dimensions of the picture?
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The length of a picture is 1 inch less than twice its width. The frame around the picture has a uniform width of 2 inches and an area of 96 square inches. What are the dimensions of the picture?
OUTSIDE FRAME DATA:
Let the width be "x"
Then the length is "2x-1" inches.
PICTURE DATA:
width = x-2(2)=x-4 inches
length = 2x-1-2(2)= 2x-5 inches
EQUATION:
Picture area = length * width = 96 sq. in.
(x-4)(2x-5)=96
2x^2-13x+20=96
2x^2-13x-76=0
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=777 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 10.2186799323832, -3.71867993238318. Here's your graph:

Only x=10.22 is a usuable answer.
So, dimensions of the picture are:
width = x-2=8.22 inches
length = 2x-5=15.44 inches
cheers,
Stan H.

RELATED QUESTIONS

Hello, I need help with this problem: The length of a picture is one inch less... (answered by ankor@dixie-net.com)
The length of a picture is 1 inch less than twice its width. The frame around the... (answered by stanbon)
A picture’s length is 6in less than twice its width. A uniform frame of 2in surrounds... (answered by ankor@dixie-net.com)
A picture frame has a perimeter of 100 cm. Its width is 4 cm less than twice its length.... (answered by thejackal)
a. The length of a picture frame is 3 inches more than its width. The perimeter of the... (answered by Cromlix)
The length of a picture frame is 2 inches greater than its width. If the area of the... (answered by rwm)
a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm.... (answered by nerdybill)
a picture frame has a perimeter of 62 inches. the difference between the length and twice (answered by macston)
the length of a rectangular picture is 4 less than twice its width. it is placed in a... (answered by ankor@dixie-net.com)