Question

A right triangle has vertices (−7,9),(3,9),(−7,−15). Find the perimeter of the triangle. please help. a simple formula will due. and an explanation

Answer 1

Answer:

  60

Step-by-step explanation:

If the sides of the triangle have lengths a, b, c, the perimeter is their sum:

  P = a + b + c

Any of the side lengths can be found using the distance formula. However, since two of the sides are aligned with the axes, their lengths are easily found by subtracting coordinates.

If the points are labeled A, B, C, in order, then the two right-angle sides are ...

  c = AB = 3 -(-7) = 10

  b = AC = 9 -(-15) = 24

The Pythagorean theorem tells you that you can find the third side from the relation ...

  a² = b² +c²

  a² = 10² +24² = 676

  a = √676 = 26

Now, we can use these values in the formula for the perimeter:

  P = a + b + c = 26 + 24 + 10

  P = 60

The perimeter of the triangle is 60 units.