2018 AMC 10B Problems/Problem 4
Problem
A three-dimensional rectangular box with dimensions ,
, and
has faces whose surface areas are
,
,
,
,
, and
square units. What is
+
+
?
Solution
Let be the length of the shortest dimension and
be the length of the longest dimension. Thus,
,
, and
.
Divide the first to equations to get
. Then, multiply by the last equation to get
, giving
. Following,
and
.
The final answer .