We assume the triangle is a right triangle. In a 30°-60°-90° triangle, the longest side is twice the length of the shortest.
... 4x = 2(√(x/2))
... 2x = √(x/2) . . . . . . divide by 2
... 4x² = x/2 . . . . . . . . square both sides
... 8x² - x = 0 . . . . . . . multiply by 2, subtract x
... x(8x -1) = 0 . . . . . . . factor
... x = 0 . . . or . . . x = 1/8 . . . . . . values of x that make the factors zero
The first case (x=0) is a "degenerate" case and is not useful. The entire triangle is a single point in that case.
The value of x is ...
... x = 1/8
The answer is x=37/5! In decimal form it is x=7.4
Surface area = 2419.34 square meters
Solution:
The base is a heptagon. It have 7 sides.
Area of base (B) = 
Area of base (B) = 439.67 m²
Perimeter of base (P) = Number of sides × side length of base
= 7 × 11
Perimeter of base (P) = 77 m
Distance between bases = 20 m
Surface area of the prism = 2B + PH
= 2 × 439.67 + 77 × 20
= 879.34 + 1540
= 2419.34 m²
Surface area = 2419.34 square meters
The answer is 13x10
When you factor out the equation and find the roots
x= 13,10
The last one should be right :)
