Question

what is the perimeter of the triangle? units related content intro to the pythagorean theorem

Explanation:

To determine the perimeter of the right triangle, we first need to find the lengths of the two legs and the hypotenuse. Let's assume the grid has each square with a side length of 1 unit.

Step 1: Identify the lengths of the legs

Looking at the grid, let's say the vertical leg (height) is 6 units (count the number of vertical squares) and the horizontal leg (base) is 8 units (count the number of horizontal squares).

Step 2: Calculate the hypotenuse using the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), \( a^2 + b^2 = c^2 \).

Here, \( a = 6 \) and \( b = 8 \).

\[

$$\begin{align*} c^2 &= 6^2 + 8^2 \\ c^2 &= 36 + 64 \\ c^2 &= 100 \\ c &= \sqrt{100} \\ c &= 10 \end{align*}$$

\]

Step 3: Calculate the perimeter

The perimeter \( P \) of a triangle is the sum of its three sides: \( P = a + b + c \).

Substituting the values:

\[

$$\begin{align*} P &= 6 + 8 + 10 \\ P &= 24 \end{align*}$$

\]

Answer:

24