1. **State the problem:** We have a right triangle with legs measuring 6.6 yards and 6.4 yards. We need to find the perimeter, which is the sum of all three sides.
2. **Formula used:** The Pythagorean theorem states that in a right triangle, the square of the hypotenuse $b$ is equal to the sum of the squares of the legs:
$$b^2 = a^2 + c^2$$
where $a=6.6$ yd and $c=6.4$ yd.
3. **Calculate the hypotenuse:**
$$b^2 = 6.6^2 + 6.4^2$$
$$b^2 = 43.56 + 40.96$$
$$b^2 = 84.52$$
4. **Find $b$ by taking the square root:**
$$b = \sqrt{84.52}$$
$$b \approx 9.2 \text{ yards}$$
5. **Calculate the perimeter $P$:**
$$P = a + c + b$$
$$P = 6.6 + 6.4 + 9.2$$
$$P = 22.2 \text{ yards}$$
6. **Answer:** The perimeter of the triangle is approximately 22.2 yards, rounded to the nearest tenth.
Pythagorean Perimeter Ced4E1
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.