The legs of a right triangle measure 16 cm and 23 cm.  What is the approximate perimeter of the triangle?

To find the approximate perimeter of a right triangle with legs of 16 cm and 23 cm, we can follow these steps:

### Step 1: Find the hypotenuse
We use the Pythagorean theorem, which states:
\[
c = \sqrt{a^2 + b^2}
\]
where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.

For this problem:
\[
a = 16 \, \text{cm}, \quad b = 23 \, \text{cm}
\]
\[
c = \sqrt{16^2 + 23^2} = \sqrt{256 + 529} = \sqrt{785} \approx 28.02 \, \text{cm}
\]

### Step 2: Find the perimeter
The perimeter \( P \) of the triangle is the sum of the lengths of all three sides:
\[
P = a + b + c = 16 + 23 + 28.02 \approx 67.02 \, \text{cm}
\]

Thus, the approximate perimeter of the triangle is **67.02 cm**.

Would you like more details or have any questions?

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Here are 8 related questions:
1. How do you calculate the area of this right triangle?
2. What would happen if one leg was twice the length of the other?
3. How can the Pythagorean theorem be applied in three dimensions?
4. What is the relationship between the angles in a right triangle?
5. How do you find the altitude of a right triangle?
6. How can trigonometric ratios help in finding the angles of the triangle?
7. Can the perimeter be calculated using trigonometry instead of the Pythagorean theorem?
8. What happens to the perimeter if the triangle is scaled by a factor of 2?

Tip: The hypotenuse is always the longest side in a right triangle.

Learn how to calculate the approximate perimeter of a right triangle with legs 16 cm and 23 cm. Step-by-step solution using the Pythagorean theorem and perimeter formula. Suitable for Grades 7-9 students.

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