The perimeter of a triangle is calculated by adding its three side lengths.
We are given only one side length of the triangle. The two remaining measurements are missing. However, the shorter missing side length is the leg of the right triangle formed to the right-hand side of the figure.
For this right triangle, the length of its leg is 5m and the length of the hypotenuse is 10m. Let's substitute these values in the Pythagorean Theorem and solve for the leg h.
Note that we only kept the principal root when solving the equation because h is the length of a side of a triangle and it must be non-negative. We found that the length of the leg is 5sqrt(3)m. This is also the length of one of the missing side lengths of the given triangle.
Note that the shortest side of the triangle and two horizontal segments form a linear pair. Thus, both angles are right angles and the side of the triangle whose length is missing is the hypotenuse of the right triangle.
For this right triangle, the lengths of the legs are 5sqrt(3)mm and 30mm. Let's substitute these values in the Pythagorean Theorem and solve for the hypotenuse c.
Again, we only kept the principal root when solving the equation because c is the length of the hypotenuse and it must be non-negative. We found that the length of the hypotenuse is 5sqrt(39)m. This is also the length of the third missing side length of the given triangle.
Now we can add the three side lengths to obtain the perimeter.
Perimeter: 5sqrt(3)+30+5sqrt(39) ≈ 69.9m.
Area
The area of a triangle is half the product of its base and its height. The height is the altitude perpendicular to whichever side is being used as the base.
In the given triangle, we can see that the base is 30m and that the height is 5sqrt(3)m. We can substitute these two values in the formula for the area of a triangle and simplify.
