The perimeter of a triangle is calculated by adding its three side lengths.
We are given that lengths of two sides of the triangle are 5 inches and 21.5 inches, but we are missing the third measurement. Note that the side whose length is missing is the hypotenuse of the right triangle formed to the left-hand side of the figure.
For this right triangle, the lengths of the legs are 8 inches and 15 inches. Let's substitute these values in the Pythagorean Theorem and solve for the hypotenuse c.
Note that we only kept the principal root when solving the equation because c is the length of a side of a triangle and it must be non-negative. We found that the length of the hypotenuse is 17 inches. This is also the length of the missing side of the given triangle.
Now we can add the three side lengths to obtain the perimeter.
Perimeter: 17+5+21.5=43.5 in.
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 5 inches and the height is 8 inches. We can substitute these two values in the formula for the area of a triangle and simplify.
