Emily wants to hang a painting in a gallery but the painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. The frame must have an equal width of x on each side. Which quadratic equation represents the area of the painting and frame combined?

4x2 + 22x − 1 = 0

4x2 + 22x + 31 = 0

x2 + 11x − 1 = 0

x2 + 11x + 31 = 0

Question

Emily wants to hang a painting in a gallery but the painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. The frame must have an equal width of x on each side. Which quadratic equation represents the area of the painting and frame combined?



 4x2 + 22x − 1 = 0

 4x2 + 22x + 31 = 0

 x2 + 11x − 1 = 0

 x2 + 11x + 31 = 0

anonymous · Answer

http://learn.flvs.net/webdav/assessment_images/educator_algebra1_v10/09_10_69.jpg

anonymous · Answer

x is the width of the frame. x has to be added twice to each dimension SOO
 the dimensions with the frame are (5 + 2x) and (6 + 2x)
 The area is (5 + 2x)(6 + 2x) and must be = 31

 30 + 10x + 12x + 4x² = 31
 4x² + 22x + 30 - 31 = 0
 4x² + 22x - 1 = 0

anonymous · Answer

Thank you