Given triangle JKL on the coordinate plane.
J= (1,7) L=(1,1) K= (6,1)
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The length of side JK is
The length of side LK is .
The length of side JL is .
The perimeter of triangle JKL in simplest radical form
.
Skip to navigation
To find the length of a side in a triangle, we can use the distance formula.
The distance formula is given by: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the length of side JK:
JK = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((6 - 1)^2 + (1 - 7)^2)
= sqrt(5^2 + (-6)^2)
= sqrt(25 + 36)
= sqrt(61)
So the length of side JK is sqrt(61).
Similarly, we can find the length of side LK:
LK = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((6 - 1)^2 + (1 - 1)^2)
= sqrt(5^2 + 0^2)
= sqrt(25 + 0)
= sqrt(25)
= 5
So the length of side LK is 5.
To find the length of side JL, we can use the same formula:
JL = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((1 - 1)^2 + (1 - 7)^2)
= sqrt(0^2 + (-6)^2)
= sqrt(0 + 36)
= sqrt(36)
= 6
So the length of side JL is 6.
Now, to find the perimeter of triangle JKL, we add up the lengths of all three sides:
Perimeter = JK + LK + JL
= sqrt(61) + 5 + 6
= sqrt(61) + 11
So the perimeter of triangle JKL in simplest radical form is sqrt(61) + 11.