Quadratic Equation

Question

a photograph measuring 16cm by 12cm is to be surrounded by a mat before framing. The width of the mat is to be the same on all sides of the photograph. The area of the mat is equal to the area of the photograph. Find the width of the mat, to the nearest tenth of a centimeter.

the answer is 2.85cm

Answer 1

Area = 4x^2 (the 4 corners) + 2(12x) + 2(16x) (the other two sides times 2)

= 4x^2 + 56x = 12(16)

divide by 4

x^2 +14x -48 = 0

use the quadratic formula

x = -14/2 + or - (1/2)sqr(196+192)

= -7 + 19.7/2 = -7+ 9.85 = 2.85