Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Square with an inner frame with height of 2ft on the left frame and width of 3ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.

x2 + 14x − 2 = 0
2x2 + 10x − 7 = 0
3x2 + 12x − 7 = 0
4x2 + 10x − 1 = 0

Question

Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Square with an inner frame with height of 2ft on the left frame and width of 3ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.

 x2 + 14x − 2 = 0
 2x2 + 10x − 7 = 0
 3x2 + 12x − 7 = 0
 4x2 + 10x − 1 = 0

anonymous · Answer

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anonymous · Answer

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mathmate · Answer

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Area of picture = 2*3=6 sq. ft
Area of picture + frame = 6+7=13 sq.ft
width of picture + frame  = 2+x+x = 2+2x
length of picture + frame = 3+x+x = 3+2x
So use the equation 
(2+2x)(3+2x)=13
and simplify