SOLUTION: A picture 9 inches and 8 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the boarder be if the area of t

Algebra ->  Finance -> SOLUTION: A picture 9 inches and 8 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the boarder be if the area of t      Log On


   

Question 1108943: A picture 9 inches and 8 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the boarder be if the area of the border is 124.
I did this question for a quiz and I got it wrong. The answer that I got was 9.

Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the width under the question.


Then the outer dimensions are 9+2x and 8+2x.


The condition says


(9+2x)*(8+2x) - 9*8 = 124    (the difference of the two areas is 124 square inches)


16x + 18x  + 4x^2 = 124

34x + 4x^2 = 124

2x^2 + 17x - 62 = 0


x%5B1%2C2%5D = %28-17+%2B-+sqrt%2817%5E2+%2B+4%2A2%2A62%29%29%2F%282%2A2%29 = %28-17+%2B-+28.02%29%2F4.


The only positive root makes sense  x = 2.75 (approximately).


Answer.  2.75 inches.

---------------
To see other similar solved problems, look into the lessons
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Problems on a circular pool and a walkway around it
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


--------------
Comment from student: Thank you for the help. I have a question though. Wouldn't -62 be put into the quadratic formula as 17^2-4(2)(-62)?
--------------


My response: 17^2-4(2)(-62) = 17^2 + 4*2*62.




Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Total area is area of picture (72)+ area of border (124)=196
The picture is 9 x 8. The border is x wide
The total area is therefore (9+2x)(8+2x) and that equals 196
72+34x+4x^2=196
4x^2+34x-124=0
2x^2+17x-62=0
quadratic formula is x=(1/4)(-17+/- sqrt (289+496); sqrt term is sqrt(785)=28.01
x=(1/4)(-17+28.01) only positive root
x=2.75 in ANSWER for width
2x=5.50
Whole thing is 14.5*13.5=195.75, area of border is 123.75, within rounding error to 124.