Circumference: Using Pythagoras' theorem

To determine which has the larger measurement, the triangle's perimeter or the circle's circumference, we need to compute both values.

Step 1: Calculate the perimeter of the Triangle
We are given two sides of the triangle: 6 and 5. Since it's implied to be a right triangle, we apply the Pythagorean theorem to find the third side, the hypotenuse $c$:

$c = \sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}$

The perimeter $P$ of the triangle is:

$P = 6 + 5 + \sqrt{61} \approx 11 + 7.81 = 18.81$

Step 2: Calculate the circumference of the Circle
The circumference $C$ of a circle with radius $r$ is given by the formula:

$C = 2 \pi r$

Assuming the radius of the circle is equivalent to the '6' mentioned for the green line in the SVG:

$C = 2 \pi \times 6 \approx 37.7$

Step 3: Compare the Triangle's Perimeter and the Circle's Circumference
We compare the values:

• Perimeter of the Triangle: $P \approx 18.81$
• Circumference of the Circle: $C \approx 37.7$

The circumference of the circle (37.7) is greater than the perimeter of the triangle (18.81).

Therefore, the circle has the larger measurement.

Conclusion: The circle has the larger perimeter.