a⁄b = 3⁄5
S = 48
a = 3k
b = 5k
S = ((a + b)⁄2) × h
48 = ((3k + 5k)⁄2) × h
48 = (8k⁄2) × h
48 = 4k × h
h = 48 ÷ (4k)
h = 12⁄k
Точки:
A(0, 0)
B(5k, 0)
C(4k, h)
D(k, h)
Площадь ∆ABC:
S₁ = (1⁄2) × |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|
S₁ = (1⁄2) × |0(0 - h) + 5k(h - 0) + 4k(0 - 0)|
S₁ = (1⁄2) × (0 + 5k × h + 0)
S₁ = (1⁄2) × 5k × h
S₁ = (1⁄2) × 5k × (12⁄k)
S₁ = (1⁄2) × 5 × 12
S₁ = 30
Площадь ∆ADC:
S₂ = (1⁄2) × |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|
S₂ = (1⁄2) × |0(h - h) + k(h - 0) + 4k(0 - h)|
S₂ = (1⁄2) × (0 + k × h - 4k × h)
S₂ = (1⁄2) × (-3k × h)
S₂ = (1⁄2) × 3k × h
S₂ = (1⁄2) × 3k × (12⁄k)
S₂ = (1⁄2) × 3 × 12
S₂ = 18
Ответ:
30 и 18