Select the correct answer. What is the perimeter of triangle ABC ? Round answers to the nearest tenth. A. 22.4 meters B. 18 meters C. 12 meters D. 20.5 meters

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Select the correct answer. What is the perimeter of triangle ABC ? Round answers to the nearest tenth. A. 22.4 meters B. 18 meters C. 12 meters D. 20.5 meters

Answer 1

To find the perimeter of triangle ABC, we need to find the lengths of all three sides of the triangle. We already know that AB = 6m and that triangle ABC is a right triangle with ∠B = 90°. Since ∠A = ∠C = 45°, triangle ABC is also an isosceles right triangle, which means that the two legs (AB and BC) are equal in length.Step 1: Since AB = 6m, and AB = BC in an isosceles right triangle, we have BC = 6m.Step 2: To find the length of the hypotenuse AC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is:\(c^2 = a^2 + b^2\)Since AB = BC, we can use either of them for a and b:\(AC^2 = AB^2 + BC^2\)\(AC^2 = 6^2 + 6^2\)\(AC^2 = 36 + 36\)\(AC^2 = 72\)Step 3: To find AC, we take the square root of 72:\(AC = \sqrt{72}\)\(AC = \sqrt{36 \times 2}\)\(AC = \sqrt{36} \times \sqrt{2}\)\(AC = 6 \times \sqrt{2}\)Step 4: To get a decimal approximation of AC, we can use the approximate value of \(\sqrt{2}\), which is about 1.414:\(AC \approx 6 \times 1.414\)\(AC \approx 8.484\)Step 5: Now we can find the perimeter (P) of triangle ABC by adding the lengths of all three sides:\(P = AB + BC + AC\)\(P = 6m + 6m + 8.484m\)\(P = 12m + 8.484m\)\(P = 20.484m\)Step 6: Rounding to the nearest tenth, we get:\(P \approx 20.5\) metersAnswer:D. 20.5 meters

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Select the correct answer. What is the perimeter of triangle ABC ? Round answers to the nearest tenth. A. 22.4 meters B. 18 meters C. 12 meters D. 20.5 meters

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