A rectangular prism shaped toy box is 52 centimeters long. The perimeter of one side of the box is 90 centimeters. The height of the box is is twice as long as it's width. Enter the volume in cubic centimeters of the box

The volume of the toy box is 25688 cubic centimetres

Step-by-step explanation:

The 6 faces of a rectangular prism are rectangles, each two opposite faces are equal in dimensions, its dimensions are L, W, H, so two faces has dimensions L, W, two faces L, H and two faces W, H

The formula of the volume of it is V = L * W * H

∵ The toy box is shaped a rectangular prism

∵ The toy box is 52 cm long

∴ H = 52 cm

∵ The perimeter of one side is 90

- Perimeter of any rectangle is twice the sum of its dimensions

∴ Twice the sum of two dimensions of the side = 90 cm

- Divide it by 2 to find the sum of the two dimensions

∴ The sum of two dimensions = 90 : 2 = 45 cm

The sum of two dimensions is less than the height of the box, that means 45 is the sum of the other two dimensions L and W

∵ L + W = 45

∵ The height of the box is is twice as long as it's width

∴ H = 2 W

∵ H = 52 cm

∴ 52 = 2 W

- Divide both sides by 2

∴ 26 = W

∴ W = 26 cm

Substitute the value of W in the equation of the sum of the two dimensions to find L

∵ L + 26 = 45

- Subtract 26 from both sides

∴ L = 19 cm

∵ V = L * W * H

∴ V = 19 * 26 * 52

∴ V = 25688 cm³

The volume of the toy box is 25688 cubic centimetres