To find the lengths of the sides of triangle JKL on a coordinate plane and its perimeter, you would typically use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Assuming you have the coordinates of points J, K, and L, you can proceed to calculate the lengths of the sides:
- Length of side JK: Calculate using the coordinates of points J and K.
- Length of side LK: Calculate using the coordinates of points L and K.
- Length of side JL: Calculate using the coordinates of points J and L.
- Perimeter: Add the lengths of sides JK, LK, and JL.
Since you haven't provided the coordinates of triangle JKL, I can't find specific numerical values. However, once you compute the lengths based on your triangle's coordinates, you would fill in the "Response area" for each length and the perimeter with the corresponding calculations or expressions.
If you obtain lengths of the form, such as \(11\), \(61^{1/2}\), \(25^{1/2} + 36^{1/2}\), etc., you would enter those expressions into the respective input areas.
When it comes to the perimeter in simplest radical form, add all lengths, and simplify if possible:
For example, if your calculations resulted in:
- JK = \(5\)
- LK = \(11^{1/2}\)
- JL = \(25^{1/2} + 36^{1/2}\)
Then the perimeter would be:
\[ 5 + 11^{1/2} + (5 + 6) = 11 + 11^{1/2} \]
Structure your inputs accurately based on your calculations.