
One leg of a right triangle has a length of 3 m. The other sides have lengths that are consecutive integers. Find these lengths.

Let's denote the sides of the right triangle as follows:

- One leg is given as \( 3 \) m.
- The other leg will be \( x \) m.
- The hypotenuse will be \( x + 1 \) m (since the sides are consecutive integers).

Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.

Substitute the given values into the equation:
\[
3^2 + x^2 = (x + 1)^2
\]

Now, solve the equation:
\[
9 + x^2 = (x + 1)(x + 1)
\]
\[
9 + x^2 = x^2 + 2x + 1
\]
Now, subtract \( x^2 \) from both sides:
\[
9 = 2x + 1
\]
Subtract 1 from both sides:
\[
8 = 2x
\]
Divide by 2:
\[
x = 4
\]

Thus, the other leg is \( 4 \) m, and the hypotenuse is \( 4 + 1 = 5 \) m.

So, the sides of the right triangle are:
- One leg: \( 3 \) m
- Other leg: \( 4 \) m
- Hypotenuse: \( 5 \) m

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How can the Pythagorean theorem be applied to other triangles?
2. What other types of triangles can be classified based on their sides and angles?
3. How does the relationship between the sides of a right triangle change as the angles vary?
4. How can you determine if a triangle is a right triangle given its side lengths?
5. What are the properties of triangles with integer side lengths (Pythagorean triples)?

**Tip:** Always check for simple number patterns like Pythagorean triples when dealing with right triangles involving small integers.

One leg of a right triangle has a length of 3 m. The other sides have lengths that are consecutive integers. Find these lengths.

Learn how to find the consecutive integer sides of a right triangle where one leg has a length of 3 m. This problem uses the Pythagorean Theorem to solve for the other leg and hypotenuse. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation