Question

find the perimeter of the triangle with vertices D (-2,-1), E (3,2), and F(0,4). do not round before calculating the perimeter. after calculating the perimeter, round your answer to the nearest tenth.

Answer 1

We first draw the triangle in the coordinate axis, as shown in the picture.

We then circumscribe a rectangle (in fact a square) to this triangle, and we notice that each of the sides is the hypotenuse of a right triangle:

this triangles, as can be seen from the picture, have sides of length:

{5, 3}, {2, 3}, and {5, 2}.


By the pythagorean theorem, the sum of these three hypotenuses is:


`√(5^2+3^2)+ √(2^2+3^2)+ √(5^2+2^2)\\\\= √(34)+ √(13)+ √(29)\\\\\approx 5.83+ 3.6+5.385\\\\\approx14.8`


Answer: 14.8 (units)