Question

Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.

right triangle with vertices at negative 7 comma 4, negative 7 comma negative 1, and 5 comma negative 1

5 units
12 units
13 units
30 units

Answer 1

The perimeter of a right triangle is the sum of its three sides. Each side's length is the distance between its two endpoints.

The horizontal side goes from (-7, -1) to (5, -1), which is 5 - (-7) = 12 units long.

The vertical side goes from (-7, -1) to (-7, 4), which is 4 - (-1) = 5 units long.

And the hypotenuse of a right triangle with sides of lengths 5 and 12 has a length that's √(5^2 + 12^2) = √169 = 13 units long (thanks to the Pythagorean theorem!).

So, the perimeter of the triangle is 5 + 12 + 13 = 30 units.

Answer 2

Answer:To find the perimeter of the right triangle, we need to calculate the lengths of its sides.

The vertices of the right triangle are given as (-7, 4), (-7, -1), and (5, -1).

Let's calculate the lengths of the sides:

1. Side AB: This is the vertical side between the points (-7, 4) and (-7, -1). The length of AB can be found by taking the absolute difference in the y-coordinates: |4 - (-1)| = 5 units.

2. Side BC: This is the horizontal side between the points (-7, -1) and (5, -1). The length of BC can be found by taking the absolute difference in the x-coordinates: |5 - (-7)| = 12 units.

3. Side AC: This is the hypotenuse of the right triangle. It can be found using the distance formula between the points (-7, 4) and (5, -1):

AC = √[(5 - (-7))^2 + (-1 - 4)^2]

= √[12^2 + (-5)^2]

= √[144 + 25]

= √169

= 13 units.

Now, we can find the perimeter of the triangle by adding the lengths of all three sides:

Perimeter = AB + BC + AC

= 5 + 12 + 13

= 30 units.

Therefore, the perimeter of the right triangle is 30 units.

Explanation: