The surface area for a rectangular prism is given by the formula SA = 2ab + 2bc + 2ac, where a, b, and c are the lengths of the prism. If the surface area of a rectangular prism with side c measuring 12 meters is 434 square meters and length of side a measuring the same length as side b, then what is the length of side a of the rectangular prism?

We are given

We are also given  and , which allows us to rewrite the equation as

(I substituted every "b" with "a" and every "c" with "9").

The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.