Suman made a cardboard box in the form of a cube without lid if the total surface area of this box was 180 square cm what are the dimensions of the box​

if the total surface area of this box was 180 sq.cm, what are the dimensions. Since the cardboard box is a cube. Thus, its TSA = 6s2 where s stands for side of the cube. Since, this cube is without lid so we remove the area of its lid, that is, s2 from its TSA

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look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3