If the coordinates of the triangle are (2,3) , (5,3) and (5,7) ?calculate the perimeter and the area.

First we will calculate the length of the
sides.

We will use the distance formula to find the
length.

==> (2,3) and
(5.3)

==> D1 = sqrt( 2-5)62 + (3-3)62 = sqrt(9 =
3

==> (2,3)(5.7)

==> D2 =
sqrt(2-5)^2 + (3-7)^2 = sqrt(9+16) = sqrt25 = 5

==> (5.3) and
(5,7)

==> D = sqrt(5-5)^2 + (3-7)^2 = sqrt(16 =
4

Then the length of the sides are 3, 4, and
5.

Now we will calculate the
perimeter.

==> P = 3 + 4 + 5 =
12

==> Now we will calculate the
area.

==> A = sqrt ( s(s-a)(s-b) (s-c) such that s = p/2 and
a, b, c are the length of the sides.

==> A = sqrt( 6(
6-3)(6-4)(6-5) = sqrt(6*3*2*1) = sqrt36 = 6

Then the
perimeter of the triangle is 12 units and the area is 6 square
units.