Question

Nasir is laying out a garden in the shape of a right triangle. he draws it on the coordinate grid below. The three vertices of his garden are at the points A (-3,-4), B(6, -4), and C (6,8). he wants to enclose the garden with a fence that runs along its perimeter. how many feet of fencing will Nasir needs?

Answer 1

Explanation:

it is not important that the triangle is right-angled.

but the distance between each pair of points is calculated via Pythagoras

c² = a² + b²

with c being the Hypotenuse (baseline opposite of the 90° angle) = distance between the end points, and a and b are the legs (= the x and y coordinate differences of the 2 end points) of the virtual right-angled triangles between each pair of points.

so,

AB² = (6 - -3)² + (-4 - -4)² = 9² + 0² = 81

AB = 9 ft

BC² = (6 - 6)² + (8 - -4)² = 0² + 12² = 144

BC = 12 ft

and now for AC, which is because of the special case of how the main triangle is placed and oriented, the same calculation as with Pythagoras for the main right-angled triangle. but I keep showing you the point distance calculation, because this is what you will need in the future for more general triangle or other shapes calculations :

AC² = (6 - -3)² + (8 - - 4)² = 9² + 12² = 81 + 144 = 225

AC = 15 ft

so, Nasir will need

9 + 12 + 15 = 36 ft

of fencing.