An open box with a square base is to be constructed from 84 square inches of material. The height of the box is 2 inches. What are the dimensions of the box? (Hint: The surface area is S = x^2 + 4xh.)

Your surface area is: S=x^2+4xh=84 square inches and h=2 inches; so you get:
x^2+(4×2)x=84
x^2+8x-84=0 qhich is a quadratic equation. Using the quadratic formula you get two results for x:
x1=-14 and x2=6
choose the second (positive)

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abidemiokin abidemiokin · Answer 2 · 2022-06-29T11:05:42+02:00

The dimension of the box will be 2in by 6in by 6in

Total surface area of a box

The total surface area is the sum of all the surfaces of the given box. Given the surface area of the box expressed as;

S = x^2 + 4xh

Given the following

S = 84 in²

h =2in

Substitute

84 = x^2 + 4(2)x

84 = x^2 + 8x

x^2 + 8x - 84 = 0

Factorize

x^2 +8x - 84 = 0

x^2 + 14x -6x - 84 = 0

x(x+14)-6(x+14) = 0
x = 6in

Find the dimensions

The dimension of the box will be 2in by 6in by 6in

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