Exercise 54 Page 46

We calculate the perimeter of a triangle by adding together the lengths of its sides. In this triangle, one side is unknown, so we have to determine its length before we can calculate the perimeter. Since the figure is a right triangle, we can use Pythagorean Theorem to find the missing side length.

Pythagorean Theorem

For a right triangle with legs $a$ and $b,$ and hypotenuse $c,$ the following is true. $a^2+b^2=c^2$

From our figure we can read two lengths. So, we are looking for $b.$ To find it, we have to substitute $a$ and $c$ into the Pythagorean theorem and solve for $b.$ The length of the third side of our triangle is $16$ inches. Now we can calculate the perimeter from the formula. The perimeter of the triangle is $48\text{ inches}.$