I don't Think My Solution is Correct: You have 5 prints that need to be framed...

[beallison]

Question---You have 5 prints that need to be framed, with matting behind each print. The matting should create a 2 inch border around the print. You must calculate the side length of each print, so you can cut the correct size of mat.

Prints to be framed: The following square prints need to be matted.
Winter Scene – area = 360 in²
Spring Scene – area = 200 in²
Summer Scene – area = 460 in²
Fall Scene – area = 525 in²
Farm Scene – area = 660 in²

What I need to do:

• Determine the side length of various square prints when given the area of each print.
• Determine the dimensions of the matting needed to place behind each print.
• Explain how much matting is required to complete the project.

My Calculations for Print #1:
area = 360 in²

side length = √(360 in²) = 6√10 in (Don't a need to use a number with a decimal for side length?)

To allow for a 2-inch border on each side, the side length of the mat is (6√10 + 4) inches.
area of mat = (6√10 + 4)?? How do I figure out how much matting is needed? How do I determine the dimensions?

I think I am doing this incorrectly. Thank you!

 

[mmm4444bot]

You have 5 prints that need to be framed, with matting behind each print. The matting should create a 2 inch border around the print.

… Explain how much matting is required to complete the project.

I'm assuming that each print is centered on a square piece of matting. (That's the standard way to frame a print, rather than placing strips of matting around the print.)

The following square prints need to be matted.

Winter Scene: area = 360 in²
Spring Scene: area = 200 in²
Summer Scene: area = 460 in²
Fall Scene: area = 525 in²
Farm Scene: area = 660 in²

I changed your hyphens to colons. When typing mathematical statements in English, it's best not to use hyphens for punctuation because they may be misinterpreted as subtraction operators.

My Calculations for Print #1:

area = 360 in²

side length = √(360 in²) = 6√10 in

To allow for a 2-inch border on each side,

side of mat = (6√10 + 4)

area of mat = (6√10 + 4)

For this first square mat, you wrote that its side length is the same as its area. I'm sure you didn't intend to say that!

What's missing, from your expression for this mat's area?

Don't [we] need to use a number with a decimal for side length?

I think I am doing this incorrectly.

If you've been asked to estimate the total area of mat needed to frame the five prints (or to provide a rounded approximation), then you could use a calculator to get decimal approximations for each of the square roots.

If you're expected to answer with the exact area of mat needed, then you're doing it correctly.

How do I figure out how much matting is needed?

Once you have calculated the area of each mat, sum the five areas. That total area will tell you how much matting is needed (in square inches).

How do I determine the dimensions?

I don't see that they asked for the dimensions of the total matting; just report the total area. :cool:

The exact expression for the total area can be multiplied out (expanded) and the constants combined, but you will not be able to combine any radicals. I'm not sure whether you're expected to do this or not.

That is, the expression for the total area can take either of the following forms.

(A + B√C)^2 + (D + E√F)^2 + (G + H√I)^2 + (J + K√L)^2 + (M + N√O)^2

P√Q + R√S + T√U + V√W + X√Y + Z

 

[tkhunny]

Very curious. Why not produce a solution you THINK is correct? Just seems a little odd. If it IS a SOLUTION, doesn't it have to be correct?

 

[mmm4444bot]

PS: Once you have an expression for the exact area of matting needed, you could also evaluate the expression, to get a single number. Round it up to the next Integer. You could then report both answers.

What do you get? :cool: