Question

Two Identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is Kcm. If the prisms are glued together along a square base, the resulting prism has a surface area of 92/47 K cm²

What is the side length, in cm, of each square base?
A) 4 B) 8 C) 9 D) 16

Answer 1

The side length of each square obtained using the formula for the surface area of a rectangular prism is 8 cm. The option B is therefore correct

B) 8

The steps to find the correct side length of the square are as follows;

Let s represent the side length of the square, we get;

The surface area of the each prism is; 4 × s·90 + 2·s² = 360·s + 2·s²

Therefore;

360·s + 2·s² = k cm²

Surface area when the prism are glued along a square base is; A = 360·s + 360·s + 2·s²

360·s + 360·s + 2·s² = 720·s + 2·s²

720·s + 2·s² = (92/47)·k...(1)

360·s + 2·s² = k...(2)
Subtracting equation (2) from equation (1), we get;

720·s + 2·s² - 360·s + 2·s² = (92/47)·k - k

360·s = (45/47)·k

k = 376·s

360·s + 2·s² = 376·s

2·s² + 360·s - 376·s = 0

2·s² - 16·s = 0

2·s² = 16·s

2·s = 16

s = 16/2

s = 8

The square each have a side length of 8 cm