Respuesta :

Space

Answer:

x = 6

a = 18 ft

b = 36 ft

General Formulas and Concepts:

Pre-Algebra

  • Order of Operations: BPEMDAS

Algebra I

  • Factoring/Expanding
  • Solving quadratics

Trigonometry

  • Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

Given: Right triangle

a = 3x

b = 6x

c = 40

Step 2: Solve for x

  1. Substitute:                              (3x)² + (6x)² = 40²
  2. Evaluate:                                 9x² + 36x² = 1600
  3. Combine like terms:              45x² = 1600
  4. Isolate x term:                        x² = 320/9
  5. Isolate x:                                 x = (±8√5)/3
  6. Evaluate:                                x = ±5.96285

Since it is not a quadrant triangle, we must use the positive value for x.

Step 3: Find legs

Leg a

  1. Define:                    3x
  2. Substitute:              3(5.96285)
  3. Multiply:                  17.8885
  4. Round:                    18

Leg b

  1. Define:                    6x
  2. Substitute:              6(5.96285)
  3. Multiply:                  35.7771
  4. Round:                    36

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