Question

Find the perimeter of the triangle whose vertices (-2,-2), (4,-2), and (4,6) write the exact answer. Do not round

Answer 1

Answer:
`The\text{ perimeter of the triangle = 24 }`

Step-by-step explanation:

Given:

The vertices of the triangle: (-2,-2), (4,-2), and (4,6)

To find:

the perimeter of the triangle

To determine the perimeter, we will plot the points on the triangle:

We have two side lengths of the triangle. We need to get the 3rd side. Since the triangle is a right-angled triangle, we will apply Pythagoras's theorem to get the 3rd side

Hypotenuse² = opposite² + adjacent²

opposite = 8, adjacent = 6, hypotenuse = ?

`\begin{gathered} hypotenuse^2\text{ = 8}^2\text{ + 6}^2 \\ hypotenuse^2\text{ = 64 + 36} \\ hypotenuse^2\text{ = 100} \\ hypotenuse\text{ = }√(100)\text{ = 10} \end{gathered}`

The three sides are: 6, 8, 10

The perimeter of a triangle = sum of all 3 sides

`\begin{gathered} The\text{ perimeter of the triangle = 6 + 8 + 10} \\ \\ The\text{ perimeter of the triangle = 24 } \end{gathered}`

T