Question

The hypotenuse of a right triangle is 65 inches long. One leg is 3 inches shorter than the other.

Find the lengths of the legs of the triangle.

Answer 1

Using the Pythagorean theorem, we set up a quadratic equation with one leg being 3 inches shorter than the other. Solving this equation, we found that the two legs of the right triangle are approximately 39 inches and 36 inches in length.

Step-by-step explanation:

To find the lengths of the legs of the triangle, we will use 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 legs (a and b). This is expressed as a² + b² = c².

We are given that the hypotenuse is 65 inches and one leg is 3 inches shorter than the other leg.

Let's denote the longer leg as a and the shorter leg as a - 3 inches.

The equation becomes (a)² + (a - 3 inches)² = 65 inches².

Expanding the squares, we get a² + a² - 6a + 9 = 4225. Combining like terms, 2a² - 6a - 4216 = 0.

This is a quadratic equation, which can be solved for a using the quadratic formula a = (-b ± √(b² - 4ac))/(2a).

We find that a is approximately 39 inches and a - 3 is approximately 36 inches.

Therefore, the lengths of the legs of the triangle are approximately 39 inches and 36 inches.

Answer 2

To find the lengths of the legs of the right triangle, use the Pythagorean theorem. Set up an equation using the given information and solve for the unknown variable.

Step-by-step explanation:

The lengths of the legs of the right triangle can be found using the Pythagorean theorem. Let x be the length of one leg. Since the other leg is 3 inches shorter, its length would be (x-3) inches. The hypotenuse, which is 65 inches long, can be represented as √(x²+(x-3)²). To solve for x, we can use the equation x²+(x-3)² = 65². Simplifying this equation will give us the value of x.