(3(2x+1)^2 +4(2x+5)^2) /(2x+5)^2*(2x+1)^2 =7/(2x+5)(2x+1)
(3(4x^2+4x+1)+4(4x^2+20x+25)) /(2x+5)^2*(2x+1)^2 =7/(2x+5)(2x+1)
(12x^2+12x+3+16x^2+80x+100)/(2x+5)^2*(2x+1)^2 =7/(2x+5)(2x+1)
(28x^2+92x+103)/(2x+5)^2*(2x+1)^2 -7/(2x+5)(2x+1) =0
(28x^2+92x+103 -7(2x+5)(2x+1)) /(2x+5)^2*(2x+1)^2 =0
28x^2+92x+103 -7(4x^2 + 12x+5) =0
28x^2+92x+103 -28x^2 -84x -35 =0
8x +68 =0
8x = -68
x = -68 : 8
x = -8.5
1/2*sin(2π/3-4x)≥√3/4
sin(2π/3-4x)≥√3/2
sin(4x-2π/3≤-√3/2
4π/3+2πn≤4x-2π/3≤5π/3+2πn
2π+2πn≤4x≤7π/3+2πn
π/2+πn/2≤x≤7π/12+πn/2,n∈z
P = 30 м; S = 56 м²;
2*(a + b) = 30 => a + b = 15;
a * b = 56;
a = 15 - b; => (15-b) * b = 56 => b² - 15b + 56 = 0; b1 = 7; b2 = 8;
a1 = 15 - 7 = 8;
a2 = 15 - 8 = 7;
Ответ: длины сторон 7м и 8м