# Equal squares were cut at the corners from a rectangular sheet of cardboard, the length of which is 60 cm

Equal squares were cut at the corners from a rectangular sheet of cardboard, the length of which is 60 cm and the width is 40 cm, and an open box was glued from the remaining part. Find the side of the square if the base area of the box is known to be 800 cm2.

1. If we designate the X side of the square, then the width of the base of the box will be equal to the width of the cardboard sheet reduced by the side of the square on each side, which will be 40 – 2X. Likewise, the length of the base of the box will be equal to the length of the cardboard sheet reduced by the side of the square on each side, which will be 60 – 2X.

2. Knowing the area of the base of the box, create an equation and solve it.

(40 – 2X) * (60 – 2X) = 800;

2400 – 120X – 80X + 4X ^ 2 – 800 = 0;

4X ^ 2 – 200X – 1600 = 0;

X ^ 2 – 50X – 400 = 0.

D = 25 ^ 2 – 400 = 625 – 400 = 225;

X = 25 ± 15;

X1 = 10;

X2 = 40 (not suitable because 40 – 2X = -40).

Answer: the side of the square is 10 cm.

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