how wide is the border?

Question

A picture measures 15 in. by 19 in. Mallika will get it framed with a border around it so that the
total area of the picture plus the frame of uniform width is 396in^2. How wide is the border?

Answer 1

x=width of border

(15+2x)(19+2x)=396

285+38x+30x+4x²=396

4x²+68x+285=396

4x²+68x+285-396=0

4x²+68x-111=0

4*111=444

444=2*2*3*37 and 2*3=6, 2*37=74, 74-6=68

factor

(2x+37)(2x-3)=0

2x-3=0

2x=3

x=1.5 inches

check: 15+1.5+1.5=18, 19+1.5+1.5=22, 18*22=396