Please explain how to do this problem. The answer says the answer is 2.43 inches, but I don't get it.
A school wants to take out an ad in the paper congratulating a basketball on a successful season. The area of the photo will be half the area of the entire ad. The photo is 7 in. wide and 5 in. long. How wide will the border be?
6 answers
since you give no idea on the available space, that's hard to say. However, a border of 2.43 inches around a 5x7 photo will occupy an area of (5+2*2.43)(7+2*2.43) = 116.94 in^2, which is more than twice as big as the photo.
If you think about
Prentice Hall Algebra 1
9 - 6
then :
The area of the photo will be half the area of the entire ad.
Area of the photo = 7 * 5 = 35 in ^ 2
that is one half the area of the paper.
So area of the paper = 70 in ^ 2
Now you must solve equation :
( 7 + x ) ( 5 + x ) = 70
5 * 7 + 5 * x + x * 7 + x * x = 70
35 + 5 x + 7 x + x ^ 2 = 70
x ^ 2 + 12 x + 35 = 70 Subtract 70 to both sides
x ^ 2 + 12 x + 35 - 70 = 70 - 70
x ^ 2 + 12 x - 35 = 0
The solutions are :
- 6 - sqrt ( 71 ) = -14.43
and
sqrt ( 71 ) - 6 = 2.43
Wide cant be negative, so wide = 2.43 in
P.S.
If you don't know how to solve equation
x ^ 2 + 12 x - 35 = 0
then in google type :
quadratic equation online
When you see list of results click on :
Free Online Quadratic Equation Solver: Solve by Quadratic
When page be open in rectangle type :
x ^ 2 + 12 x - 35 = 0
and click option :
solve it
You will see solution step by step
Prentice Hall Algebra 1
9 - 6
then :
The area of the photo will be half the area of the entire ad.
Area of the photo = 7 * 5 = 35 in ^ 2
that is one half the area of the paper.
So area of the paper = 70 in ^ 2
Now you must solve equation :
( 7 + x ) ( 5 + x ) = 70
5 * 7 + 5 * x + x * 7 + x * x = 70
35 + 5 x + 7 x + x ^ 2 = 70
x ^ 2 + 12 x + 35 = 70 Subtract 70 to both sides
x ^ 2 + 12 x + 35 - 70 = 70 - 70
x ^ 2 + 12 x - 35 = 0
The solutions are :
- 6 - sqrt ( 71 ) = -14.43
and
sqrt ( 71 ) - 6 = 2.43
Wide cant be negative, so wide = 2.43 in
P.S.
If you don't know how to solve equation
x ^ 2 + 12 x - 35 = 0
then in google type :
quadratic equation online
When you see list of results click on :
Free Online Quadratic Equation Solver: Solve by Quadratic
When page be open in rectangle type :
x ^ 2 + 12 x - 35 = 0
and click option :
solve it
You will see solution step by step
Thanks Bosnian!
You're welcome.
Good work, but if x = 2.43, the border is only half that wide, if it surrounds the entire picture. I guess in this case it does not.
yeaaaaaasssss