Question

The hypotenuse of a right triangle is 7 ft long. One leg is 1.4 ft longer than the other

leg. Find the lengths of the legs.
4.2 ft² and 5.6 ft²
1.4 ft and 5.6 ft
1.4 ft² and 5.6 ft²
4.2 ft and 5.6 ft

Answer 1

Using the Pythagorean theorem, the legs of the right triangle with a hypotenuse of 7 ft and one leg longer than the other by 1.4 ft are found to be approximately 4.2 ft and 5.6 ft in length.

Step-by-step explanation:

The problem requires us to find the lengths of the legs of a right triangle when given the length of the hypotenuse and the relationship between the legs. The lengths can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), or a² + b² = c². Given that the hypotenuse (c) is 7 ft and one leg is 1.4 ft longer than the other leg, we can set up the following system of equations:

• Let x be the length of the shorter leg.
• Then the longer leg is x + 1.4 ft.
• The equation representing the Pythagorean theorem is x² + (x + 1.4)² = 7².

Solving for x:

• First, square the hypotenuse: 7² = 49.
• Next, expand the square of the longer leg: (x + 1.4)² = x² + 2.8x + 1.96.
• Combine like terms:
  • 2x² + 2.8x + 1.96 = 49
  • 2x² + 2.8x - 47.04 = 0
• Divide the entire equation by 2 to simplify:
  • x² + 1.4x - 23.52 = 0
• Factoring or using the quadratic formula, we find that x ≈ 4.2.
• Thus, the longer leg is x + 1.4 ≈ 5.6 ft.

The legs of the triangle are approximately 4.2 ft and 5.6 ft in length, satisfying the conditions of the problem.