A matte of uniform width is to be placed around a painting so that the area of the matted surface is equal to the area of the painting. If the dimensions of the painting are 15 cm and 10 cm, find the width of the matte. The answer is supposed to be 2.5 cm but I keep getting 12.5.

Answer 1

let the width of the matte be x all around
so the width of the whole picture = 10+2x
and the length is 15+2x

area of whole picture = (10+2x)(15+2x)
area of picture = 10(15) = 150
area of matte only = (10+2x)(15+2x) - 150

so (10+2x)(15+2x) - 150 = 150
150 + 20x + 30x + 4x^2 - 300 = 0
4x^2 + 50x - 150 = 0
2x^2 + 25x - 75 = 0
(2x - 5)(x + 15) = 0
x = -15 , not possible or x = 5/2 = 2.5

Can you find your error?

Answer 2

@reiny
what did you do to get from 2x^2 + 25x - 75 = 0
to (2x - 5)(x+15) ?