Subjects geometry

Pythagorean Perimeter Ced4E1

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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.