Emily wants to hang a painting in a gallery. The painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Question

anonymous · Answer

total area=31 square feet.
if the thickness of the frame is x feet, what's the total length of the frame?
that will be (6+2x) feet, similarly the total width will be (5+2x) feet
so, the total area: (6+2x)(5+2x)=31

anonymous · Answer

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anonymous · Answer

That's what I got. But the answer choices confuse me.

4x2 + 22x - 1 = 0

 4x2 + 22x + 31 = 0

 x2 + 11x - 1 = 0

 x2 + 11x + 31 = 0

anonymous · Answer

yeah, multiply the two term on the left hand side and then make the right hand side zero, you will get the answer

anonymous · Answer

I used FOIL and got 26x + 30 Am I not supposed to use that method?

anonymous · Answer

multiply 5+2x with 6+2x, what will it be?

anonymous · Answer

I got 26x + 30

anonymous · Answer

Ooh! Wait!

anonymous · Answer

(5+2x)(6+2x)=5*(6+2x)+2x*(6+2x)

anonymous · Answer

I see what I did wrong

anonymous · Answer

yeah, try it yourself

anonymous · Answer

you will see one of the answers match just fine!

anonymous · Answer

Well, I got 4x^2 + 22x + 30 and the closest answer is b.

anonymous · Answer

you missed the right hand side, 4x^2+22x+30=31, not 0

anonymous · Answer

(6+2x)(5+2x)=31, right?

anonymous · Answer

Oh I see now.

anonymous · Answer

Simplify the following:$$(2 x+6) (2 x+5)-31 $$

anonymous · Answer

4x^2 + 22x -1

anonymous · Answer

Which would be answer A? Did I do that right?