Question

2 shorter sides of a right triangle having length of 16 m and 8 cm what is the perimeter of the triangle

Answer 1

Given a right triangle with the two shorter sides measuring 16 meters and 8 centimeters, we need to convert the measurement of the shorter side to a consistent unit. Let's convert 8 centimeters to meters:

1 meter = 100 centimeters,
so 8 centimeters = 8 / 100 meters = 0.08 meters.

Now, the lengths of the two shorter sides are:
- One side = 16 meters,
- The other side = 0.08 meters.

In a right triangle, the lengths of the sides satisfy the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]

where \( a \) and \( b \) are the lengths of the two shorter sides, and \( c \) is the length of the hypotenuse. Let's compute the hypotenuse:

Let \( a = 16 \) meters and \( b = 0.08 \) meters.

\[ c^2 = 16^2 + 0.08^2 \]

Calculating each term:
\[ 16^2 = 256 \]
\[ 0.08^2 = 0.0064 \]

Adding these together:
\[ c^2 = 256 + 0.0064 \]
\[ c^2 = 256.0064 \]

Taking the square root of both sides to find \( c \):
\[ c = \sqrt{256.0064} \approx 16.0002 \text{ meters} \]

Now, the perimeter of the triangle is the sum of the lengths of all three sides:
\[ \text{Perimeter} = a + b + c \]
\[ \text{Perimeter} = 16 + 0.08 + 16.0002 \]
\[ \text{Perimeter} \approx 32.0802 \text{ meters} \]

Therefore, the perimeter of the triangle is approximately 32.0802 meters.