Answer:
The dimension of the triangle is 4.144 m and the dimension of the square is 2.392 m
Step-by-step explanation:
let a side of the equilateral triangle = x
let a side of square = y
3x + 4y = 22
4y = 22 - 3x
[tex]y = \frac{11}{2} -\frac{3x}{4}[/tex]
subjective function, the total area is given by;
[tex]f(x,y) = \frac{x^2\sqrt{3} }{4} +y^2[/tex]
[tex]f(x) = \frac{x^2\sqrt{3} }{4} + (\frac{11}{2} -\frac{3x}{4})^2\\\\f(x) = \frac{x^2\sqrt{3} }{4} +\frac{121}{4} -\frac{33x}{4} +\frac{9x^2}{16} \\\\f(x)' = \frac{x\sqrt{3} }{2} -\frac{33}{4} +\frac{9x}{8} \\\\\frac{x\sqrt{3} }{2} -\frac{33}{4} +\frac{9x}{8}=0\\\\\frac{x\sqrt{3} }{2} + \frac{9x}{8} =\frac{33}{4}\\\\\frac{4x\sqrt{3} +9x}{8} = \frac{33}{4}\\\\4x\sqrt{3} +9x = 66\\\\x(4\sqrt{3} +9) = 66\\\\x(15.928) = 66\\\\x = \frac{66}{15.928}\\\\x = 4.144 \ m[/tex]
solve for y
[tex]y = \frac{11}{2} -\frac{3x}{4}\\\\y = \frac{11}{2} -\frac{3*4.144}{4}\\\\y = 5.5-3.108\\\\y = 2.392 \ m[/tex]
Therefore, the dimension of the triangle is 4.144 m and the dimension of the square is 2.392 m
