devise a plan and solve, two similiar prism have a total surface area of 100cm (square and 225 cm (square)?

Question

two similar prisms have total surface areas of 100cm(square) and 225 cm(square). if the smaller prism has a height of 10cm, what is the height of the larger prism.

Answer 1

Since the prisms are similar, the expansion factor is the square root of the ratio of the areas.

Thus each dimension of the small prism is increased by a factor of (225/100)^1/2 = 1.5

Therefore the new height is (1.5)(10) = 15 cm