Question

A picture needs a border of uniform width to surround it before it is framed. For the most pleasing effect the border needs to have the exact same area as the picture to be framed. If the original picture is 12 em by 17 cm, determine the required width of the border, rounded to twe decimal places.

Answer 1

width = 2.93 cm

Explanation:

Area of picture = 12 x 17 = 204

let x = width of border

2(17 + 2x)(x) + 2(12x) = 204

34x + 4x² + 24x - 204 = 0

4x² + 58x - 204 = 0

Use quadratic formula to find x: a = 4, b = 58, c = -204

x = 2.93, -17.43 disregard the negative root

x = 2.93 cm