In the image, you are tasked with finding the perimeter and area of a right triangle. The triangle has the following given dimensions:

• One leg is 48 units.
• Another leg is 20 units.
• The hypotenuse is unknown.

To find the perimeter:

1. Use the Pythagorean theorem to determine the hypotenuse. The formula is: $c = \sqrt{a^2 + b^2}$ where $a = 48$ and $b = 20$.

2. The perimeter of the triangle is the sum of all three sides: $\text{Perimeter} = a + b + c$

To find the area:

The formula for the area of a right triangle is: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ In this case, the base is 48 units and the height is 20 units.

Let me calculate these values for you.The calculations for the triangle yield the following results:

• Perimeter: 120 units
• Area: 480 square units

Would you like any further details or explanations?

Here are some related questions to explore:

1. How is the Pythagorean theorem derived?
2. What happens to the area if the base or height is doubled?
3. Can you find the perimeter and area of other types of triangles (like equilateral)?
4. What is the relationship between perimeter and area in geometric shapes?
5. How can you apply the Pythagorean theorem to 3D shapes?

Tip: Always double-check the units when calculating area and perimeter to ensure accuracy!