The perimeter of a triangle is calculated by adding its three side lengths.
We are given one side length of the triangle, 29mm, but are missing the other two. Note that one of the sides is a leg of the right triangle formed to the left of the diagram.
For this right triangle, the length of the second leg is 13mm and the length of the hypotenuse is 18mm. Let's substitute these values in the Pythagorean Theorem and solve for the leg h.
Please note that since h is the leg of a right triangle it must be non-negative, which is why we only kept the principal root when solving the equation. The length of the second leg is 12.45mm to the nearest tenth. This is also the length of the second side of the triangle for which we want to find the perimeter.
Note that the shortest side of the triangle and two horizontal segments form a linear pair. Thus, both angles are right angles. Therefore, the side of the given triangle whose length is still missing is its hypotenuse.
For this right triangle, the lengths of the legs are 29mm and 12.45mm. Let's substitute these values in the Pythagorean Theorem and solve for the hypotenuse d.
Please note that since d is the hypotenuse of a right triangle it must be non-negative, which is why we only kept the principal root when solving the equation. The length of the hypotenuse is about 31.56mm. This is also the length of the third side of the triangle for which we want to find the perimeter.
Now we can add the three side lengths to obtain the perimeter.
Perimeter: 12.45+29+31.56≈ 73mm
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 29mm and that the height is 12.45mm. We can substitute these two values in the formula for the area of a triangle and simplify.
