The length of the rectangular prism is also the length of the triangular prism. Let the length be x
Surface area of composite figure = area of each face
Considering the rectangular prism,
Area = base = 3 * x = 3x
Area of both sides = 2 * 5 * 3 = 30
Area of 2 front faces = 2 * x * 5 = 10x
Considering the triangular prism,
Area of rectangular base = 4 * x = 4x
Area of rectangular side = 5 * x = 5x
Area of 2 triangular faces = 2 * 1/2 * 4 * 3 = 12
From the information given,
Surface area of fiigure = 482 square inches
Thus,
3x + 30 + 10x + 4x + 5x + 12 = 482
Collect like terms. It becomes
3x + 10x + 4x + 5x = 482 - 30 - 12
22x = 440
x = 440/22
x = 20
The length of the prism is 20 inches
