How wide should the border be in order to cover half the area inside the frame?

Question

Billy is preparing a picture frame. The frame measures 9 inches by 12 inches. Billy wants to put a uniform border inside the frame.

Answer 1

9 by 12 inch frame

need a uniform border that = same area as picture inside the frame = area 1/2 of 9x12 = 54 in^2

it helps to draw a diagram, at least a rough sketch

left&right border area + top&bottom border area - the 4 square corners = 1/2 total area

2(9x) + 2(12x)- 4x^2= 54

18x +24x -4x^2 = 54

2x^2 -21x +27=0

factor

(2x -3)(x-9) = 0

x = 9, or 3/2 inches

reject 9 as too large

uniform border width = 1 1/2 inches