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The attached figure represents the cardboard (10inches by 12 inches) and the squares that should be cut to make the box.
let the length of the square = x
So , the length of the box = L = 12 - 2x
the width of the box = W = 10 - 2x
And, the area = L * W = 80 ⇒(given)
∴ L * W = (12-2x)(10-2x) = 80
∴ (12 - 2x)(10-2x) =80
4x² - 44x + 120 = 80 ⇒ multiply the brackets
4x² - 44x +120 - 80 = 0 ⇒ make all variables in one side
4x² - 44x + 40 = 0 ⇒ sum the similar
x² - 11x +10 = 0 ⇒ solve by analysis
(x-1)(x-10) = 0
∴ x = 10 (rejected because the cardboard length = 10 inch)
OR x = 1
∴ the size of the square should be cut from each corner = 1 inch by 1 inch
let the length of the square = x
So , the length of the box = L = 12 - 2x
the width of the box = W = 10 - 2x
And, the area = L * W = 80 ⇒(given)
∴ L * W = (12-2x)(10-2x) = 80
∴ (12 - 2x)(10-2x) =80
4x² - 44x + 120 = 80 ⇒ multiply the brackets
4x² - 44x +120 - 80 = 0 ⇒ make all variables in one side
4x² - 44x + 40 = 0 ⇒ sum the similar
x² - 11x +10 = 0 ⇒ solve by analysis
(x-1)(x-10) = 0
∴ x = 10 (rejected because the cardboard length = 10 inch)
OR x = 1
∴ the size of the square should be cut from each corner = 1 inch by 1 inch