PLEASE HELP WITH THIS ONE QUESTION A 60 cm by 80 cm photo is to be surrounded with a matting of equal width. The photo and matting is to be covered by a 1 m^2 sheet of expensive glass. Find the width of the matting.

We know the area = width height. So we can set up this equation, where x is the unknown space between the entire frame and the photo:
(60cm + x) (80cm + x) = 1m^2

And then convert the m^2 to cm^2 so it’s all the same units:
1m^2 = 1m x 1m = 100cm x 100cm = 10000cm^2

So we get:
(60cm + x) (80cm + x) = 10000cm^2

Then solve for x:

(60cm + x) (80cm + x) = 10000cm^2
4800 + 140x + x^2 = 10000
x^2 + 140x - 5200 = 0

Using the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a

x = ( -140 +/- sqrt(140^2 - 4(1)(-5200)) )/ 2(1)
x = ( -140 +/- sqrt(19600 -(-20800)) )/ 2
x = ( -140 +/- sqrt(40400)) / 2

x = ( -140 + 200.9975 )/ 2
x = 30.49875

x = (140 - 200.9975)/2
x = -60.9975

So we get:
x = 30.49875 or -60.9975

The width of the matting is the part of the width underneath the photo (60cm) plus the spacing between the photo and the border, x (which would have to be 30.5 because it doesn’t make sense as a negative). So it’s:
60cm+30.50cm = 90.50 cm

The width of the matting is 90.50cm.

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