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

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Question: The lengths of the sides of triangle GHI 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:

This is a right triangle. Area = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm².

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

The lengths of the sides of triangle GHI 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 triangle GHI, which are 5 cm, 12 cm, and 13 cm.
Step 2: Check if this triangle is a right triangle. A right triangle has one angle that is 90 degrees.
Step 3: Use the Pythagorean theorem (a² + b² = c²) to check if 5² + 12² = 13².
Step 4: Calculate 5², which is 25, and 12², which is 144. Add them together: 25 + 144 = 169.
Step 5: Calculate 13², which is also 169. Since 25 + 144 = 169, this confirms that triangle GHI is a right triangle.
Step 6: Identify the base and height of the triangle. We can use 5 cm as the base and 12 cm as the height.
Step 7: Use the formula for the area of a triangle: Area = 1/2 * base * height.
Step 8: Substitute the values into the formula: Area = 1/2 * 5 * 12.
Step 9: Calculate the area: 1/2 * 5 = 2.5, then 2.5 * 12 = 30.
Step 10: Conclude that the area of triangle GHI is 30 cm².

Right Triangle Identification – The question tests the ability to recognize that the triangle with sides 5 cm, 12 cm, and 13 cm is a right triangle, allowing the use of the right triangle area formula.
Area Calculation – The question assesses the understanding of how to calculate the area of a triangle using the formula for right triangles.