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Width: x

Length: x + 8

Area: 105 m²

Find the dimension:

Area = Length × Width

105 = (x + 8) (x)

105 = x² + 8x

x² + 8x - 105 = 0

(x - 7) (x + 15) = 0

x₁ - 7 = 0 x₂ + 15 = 0

Substitute 7 for x in dimensions:

Check:

105 m² = 15 m × 7 m

105 m² = 105 m² (true)

Length: x + 8

Area: 105 m²

Find the dimension:

Area = Length × Width

**Equation:**105 = (x + 8) (x)

105 = x² + 8x

**Rewrite as quadratic equation, ax² + bx + c = 0**x² + 8x - 105 = 0

**Solve by factoring:**(x - 7) (x + 15) = 0

x₁ - 7 = 0 x₂ + 15 = 0

**x₁ = 7****x₂ = -15****Choose the positive root x = 7**Substitute 7 for x in dimensions:

**Width**: x =**7 m****Length**: x + 8 ⇒ 7 + 8 =**15 m****ANSWER: The dimensions are 15 m long and 7 m wide.**Check:

105 m² = 15 m × 7 m

105 m² = 105 m² (true)