A painting measuring 100cm by 55cm is to be framed with a matte border of uniform width surrounding the painting. the combined area of the picture and the matte is 9796cm^2. How wide is the matte border?

Answer 1

let x = the width of the border

The combined area of the picture with the border = (100+x)(55+x)

(100 + x)(55 + x) = 9796
5500 + 155x + x^2 = 9796
-4296 + 155x + x^2 = 0

Now, use the quadratic equation to find x.
x = (-b +/- sqrt(b^2 - 4ac))/2a

With these numbers, I assume a calculator is allowed.

x = 24, -179

The width of the border cannot be negative, so x = 24cm.