hey nishit can u also help me with this man?

Question

a picture with dimension 8cm x 3cm has a border x cm wide all the way around it. the area of the border is equal to the area of the picture. find the value of x correct to 3 significant figures

Answer 1

size of picture with the border:

(8+2x) * (3+2x) = 24*2 (twice the size of just picture)
24 + 22x + 4x^2 = 48
x^2 + 5.5x - 6 = 0
x=0.933 or -6.43

and since negative borders make no sense,

x = 0.933

Answer 2

area of the whole picture including border = (8+2x)(3+2x)
area of picture without border = 8 * 3 = 24
area of border = (8+2x)(3+2x) - 24

so (8+2x)(3+2x) -24 = 24
or (8+2x)(3+2x) = 48
or 4x^2 + 22x - 24 = 0
or 2x^2 + 11x - 12 = 0

or x = (-11 +/- sqrt(217))/4

Taking only the positive solution x = 0.933 correct to 3 places.