Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism..

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Bluebook Digital SAT Test 4 Module 2 (Hard) Question 21:

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 K cm. If the prisms are glued together along a square base, the resulting prism has a surface area of 92/47 K cm?. What is the side length, in cm, of each square base?

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Algebra can be reduced in this problem by equating K to the 2 missing surface areas of the square bases.

It is derived that K = 2x^2 + 360x

The 2 missing surface areas equal

2x^2 = (2/47) K
47 x^2 = K = 2x^2 + 360x
45x = 360
x = 8

OverclockingCowboy
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the surface area of a cuboid, is 2(lb+bh+hl) so when we insert the values as length and breadth as x (as they are equal), the equation would be
K =2 (x^2+90x+90x) ....(i)
K = 2x^2+360
now new dimensions after joining the prisms are
length = x
breadth = x
height= 180
now, put the values into the formula

2(x^2+180x+180x) = 92k/47
2x^2+720=92k/47
put calue of eq (i) in eq (ii)

2x^2+720= 92(2x^2+360)/7
then solve the answer is 8

mithu-smce