Polynomials and area

A

Audentes

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Hi all, Im stuck on this question. I dont know for sure where the 2.5 in applies in the equation, and Im having trouble with it
Question:
The width of a rectangular painting is 3 inches more than twice the height. A frame that is 2.5 inches wide goes around the painting.
a. Write an expression for the combined area of the painting and the frame.
b. Use the expression to find the combined area when the height of the painting is 12 inches.
c. Use the expression to find the combined area when the height of the painting is 15 inches.

im stuck with part a. For the painting, i think the expression is 2h^2+3h. I dont know though for the frame.

thank you!
flo
 
Flo Rida said:
Hi all, Im stuck on this question. I dont know for sure where the 2.5 in applies in the equation, and Im having trouble with it
Question:
The width of a rectangular painting is 3 inches more than twice the height. A frame that is 2.5 inches wide goes around the painting.
a. Write an expression for the combined area of the painting and the frame.
b. Use the expression to find the combined area when the height of the painting is 12 inches.
c. Use the expression to find the combined area when the height of the painting is 15 inches.

im stuck with part a. For the painting, i think the expression is 2h^2+3h. I dont know though for the frame.

thank you!
flo
Click to expand...
you say: "...i think the expression is 2h^2+3h" ← expression of what?
 
Flo Rida said:
The area of the painting?
Click to expand...
Why do you have a "?" in the answer?

You need to define your variables before you start. I suggest draw a sketch with all the variables and known numbers. It helps me a lot.

Height of painting = h

Length of the painting = 2*h + 3 ← The width of a rectangular painting is 3 inches more than twice the height.

Area of the painting = A1 = h * (2*h + 3)

Area of the painting+frame = A2 = (h+2*2.5) * (2*h + 3+2*2.5) ← A frame that is 2.5 inches wide goes around the painting.

Continue.....
 
Is this on the right track?
 

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Flo Rida said:
Why is 2.5 being multiplied by 2? Wouldnt that be perimeter?

If 2.5 is width/length, then it needs to be multiplied by height (h)
Click to expand...
If the shape is a rectangle (as the painting), then yes, the area is width * height. But is it a rectangle?
 
Flo Rida said:
Is this on the right track?
Click to expand...
You just have to complete your picture. Fill in the missing length and height of the large rectangle.
1618264596882.png
When you have done that, then you can see that this large rectangle is the picture+frame.
You can write down an expression for the area of the large rectangle and answer all the questions.
 
skeeter said:
painting with surrounding frame

View attachment 26421
Click to expand...
lex said:
You just have to complete your picture. Fill in the missing length and height of the large rectangle.
View attachment 26423
When you have done that, then you can see that this large rectangle is the picture+frame.
You can write down an expression for the area of the large rectangle and answer all the questions.
Click to expand...
OHHHHHHHHHH the 2.5 gets added to the 3 on both sides.. thank you for this clarity!
lev888 said:
Do you see that a "solid" rectangle (e.g. painting) and one with a hole cut out of it (frame) are NOT the same type of shape?
Click to expand...
yes, i do
 
Wait a second... i tried this method but there is no way a painting is 868 inches... i attached my work.

When it says to find the combined area of painting and frame, isnt that the same as the area of the frame?
 

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Still doesnt seem right. No way painting/frame is 45 feet.
 

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Yes. That is now correct. However, you have found an area, not a length. That is 544 square inches. That's less than 2 ft by 2 ft if it was a square.
In fact it is a rectangle 32 inches by 17 inches (2h+8 by h+5).
 
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Flo Rida said:
Wait a second... i tried this method but there is no way a painting is 868 inches... i attached my work.

When it says to find the combined area of painting and frame, isnt that the same as the area of the frame?
Click to expand...
When you refer to area of the frame, what exactly do you mean? What shape is frame? You replied that it's not a rectangle. But then you keep applying the formula for area of a rectangle.
 
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