SOLUTION: The outside of a picture frame measures 12in by 19in. 78 in^2 of the picture shows. Find the thickness of the frame.

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Question 445637: The outside of a picture frame measures 12in by 19in. 78 in^2 of the picture shows. Find the thickness of the frame.
Answer by chriswen(106)   (Show Source): You can put this solution on YOUR website!
Let x in be the thickness of the frame.
...
So,
12-2x will be the width of the picture after you take out the frame.
and 19-2x will be the length of the picture.
...
l*w=A

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (19-2x)*(12-2x) simplifies to 4*x^2-62*x+228
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (19-2x)*(12-2x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved 19 to the right of expression
It becomes .
Look at .
Moved 12 to the right of expression
It becomes .
Look at .
Expanded term %28-2%2Ax%2B12%29 by using associative property on %28-2%2Ax%2B19%29
It becomes .
Look at .
Expanded term -2%2Ax by using associative property on %28-2%2Ax%2B12%29
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes .
Look at .
Expanded term 19 by using associative property on %28-2%2Ax%2B12%29
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Eliminated similar terms highlight_red%28+-24%2Ax+%29,highlight_red%28+-38%2Ax+%29 replacing them with highlight_green%28+%28-24-38%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -62
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+62+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!




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=1444 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 12.5, 3. Here's your graph:

So therefore there are two answers 12.5 and 3.
But, this is dealing with length and area so the answer can't be a negative number. The equation was (19-2x)(12-2x) If the answer was 6 or more then the (12-2x) would make it negative or 0. So therefore, the answer is 3.
The thickness of the frame is 3 in.
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