Question

What is the perimeter of the triangle below, to the nearest tenth of an inch, if each square on the grid measures 8 inches on each side?

Answer 1

We have a right triangle with legs measuring 2 units and 4 units. Using Pythagorean Theorem, the missing length (hypotenuse), x is:
\(\displaystyle{2}^{{2}}+{4}^{{2}}={x}^{{2}}\)
\(\displaystyle{4}+{16}={x}^{{2}}\)
\(\displaystyle{20}={x}^{{2}}\)
\(\displaystyle√{20}={x}\)
So, the perimeter in terms of the number of units is:
\(\displaystyle{P}={2}+{4}+√{20}={6}+√{20}\)
Since 1 unit = 8 inches, the perimeter is:
\(\displaystyle{P}={8}{\left({6}+√{20}\right)}\)
\(P \approx 83.8\) inches