A is the point (1,2), B is (7,4) and C is (5,6). Calculate the length of each side of the triangle ABC.

Use the distance formula for finding points on the xy-plane.

Let d = distance.

d = sqrt{(x2 - x1)^2 + (y2 - y1)^2}

You must apply the above formula to find the distance between points A and B, B and C and A and C.

So, you must apply the distance formula 3 times.

Got it?

If not, write back.

emm nope i don't get it, sorry, can you do this using pythagoras??

To calculate the length of each side of triangle ABC, we can use the distance formula, which is derived from the Pythagorean theorem.

The distance formula allows us to find the distance between two points (x1, y1) and (x2, y2) in a Cartesian coordinate system. It is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the length of each side:

Length of side AB:
A = (1, 2)
B = (7, 4)

Using the distance formula:
d_AB = sqrt((7 - 1)^2 + (4 - 2)^2)
= sqrt(6^2 + 2^2)
= sqrt(36 + 4)
= sqrt(40)
= 2 * sqrt(10)

Therefore, the length of side AB is 2 * sqrt(10).

Length of side BC:
B = (7, 4)
C = (5, 6)

Using the distance formula:
d_BC = sqrt((5 - 7)^2 + (6 - 4)^2)
= sqrt((-2)^2 + 2^2)
= sqrt(4 + 4)
= sqrt(8)
= 2 * sqrt(2)

Therefore, the length of side BC is 2 * sqrt(2).

Length of side AC:
A = (1, 2)
C = (5, 6)

Using the distance formula:
d_AC = sqrt((5 - 1)^2 + (6 - 2)^2)
= sqrt(4^2 + 4^2)
= sqrt(16 + 16)
= sqrt(32)
= 4 * sqrt(2)

Therefore, the length of side AC is 4 * sqrt(2).

In summary, the lengths of the sides of triangle ABC are:
AB = 2 * sqrt(10)
BC = 2 * sqrt(2)
AC = 4 * sqrt(2)