# 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?

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?

2021-02-01
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≈83.8 inches

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$$\displaystyle{8}\frac{{3}}{{4}}{c}{m}$$