The lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm. What is the

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Question: The lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)

Options:

Correct Answer: 30 cm²

Exam Year: 2019

Solution:

Using Heron\'s formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².

The lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)

The lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)

Step 1: Identify the lengths of the sides of the triangle. They are 5 cm, 12 cm, and 13 cm.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (a + b + c) / 2, where a, b, and c are the lengths of the sides.
Step 3: Substitute the values into the formula: s = (5 + 12 + 13) / 2 = 30 / 2 = 15 cm.
Step 4: Use Heron's formula to find the area of the triangle. The formula is Area = √[s(s-a)(s-b)(s-c)].
Step 5: Calculate (s - a), (s - b), and (s - c): (15 - 5) = 10, (15 - 12) = 3, (15 - 13) = 2.
Step 6: Substitute these values into Heron's formula: Area = √[15 * 10 * 3 * 2].
Step 7: Calculate the product: 15 * 10 = 150, then 150 * 3 = 450, and finally 450 * 2 = 900.
Step 8: Find the square root of 900: √[900] = 30.
Step 9: Therefore, the area of triangle ABC is 30 cm².

Heron's Formula – A method to calculate the area of a triangle when the lengths of all three sides are known.
Triangle Properties – Understanding the properties of triangles, including the relationship between side lengths and area.