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?
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
You're welcome.
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.
Thanks Bosnian!
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
To solve this problem, we need to find the width of the border.
First, let's find the area of the entire ad. The area of a rectangle is given by the formula: Area = Length * Width. Let's denote the width of the entire ad as W and the length as L.
Given that the area of the photo is half the area of the entire ad, we can write the equation: (7 * 5) = (1/2) * (L * W).
Simplifying this equation, we have: 35 = L * W / 2.
To find the width of the border, we need to subtract the width of the photo from the width of the entire ad. So the equation becomes: W - 7 = the width of the border.
Now, we have two equations:
1) 35 = L * W / 2
2) W - 7 = the width of the border
To find the width of the border, we can substitute the value of L * W from the first equation into the second equation.
Substituting L * W / 2 for 35 in equation 2, we have:
L * W / 2 - 7 = the width of the border.
Solving for the width of the border, we get:
L * W / 2 - 7 = the width of the border.
35 / 2 - 7 = the width of the border.
17.5 - 7 = the width of the border.
10.5 = the width of the border.
Therefore, the width of the border will be 10.5 inches.