Alexei wants to hang a mirror in his boat but the mirror and frame must not have an area larger than 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation represents the area of the mirror and frame combined? (The border must have equal width on each side.)

Question

anonymous · Answer

1.	4x2 + 16x - 4.25 = 0
2.		3x2 + 5x - 19.25 = 0
3		4x2 + 16x + 15 = 0
4		2x2 + 8x - 19.25 = 0

jim_thompson5910 · Answer

Let x = width of the border

The old length is 5 feet. The new length is 5+2x feet long. We're adding 2x to represent the idea that we're adding a border with a width of x feet to each side of the length


The same idea applies to the width, the width goes from 3 feet to 3+2x feet.


The total area is then


A = LW

A = (5+2x)(3+2x)

A = 15 + 16x + 4x^2

A = 4x^2 + 16x + 15


Since this area cannot exceed 19.25 square feet, we know that the max area is 19.25 square feet


So if the area is maxed out then 19.25 = 4x^2 + 16x + 15


From here, get everything to one side and simplify


19.25 = 4x^2 + 16x + 15

0 = 4x^2 + 16x + 15-19.25

0 = 4x^2 + 16x - 4.25

4x^2 + 16x - 4.25 = 0


So the answer is choice A