A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the

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Question: A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle? (2021)

Options:

Correct Answer: 84 cm²

Exam Year: 2021

Solution:

The triangle is a right triangle (7² + 24² = 25²). The area is (1/2) * base * height = (1/2) * 7 * 24 = 84 cm².

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle? (2021)

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle? (2021)

Step 1: Identify the lengths of the sides of the triangle. They are 7 cm, 24 cm, and 25 cm.
Step 2: Check if the triangle is a right triangle by using the Pythagorean theorem. Calculate 7² + 24² and see if it equals 25².
Step 3: Calculate 7², which is 49.
Step 4: Calculate 24², which is 576.
Step 5: Add the results from Step 3 and Step 4: 49 + 576 = 625.
Step 6: Calculate 25², which is also 625.
Step 7: Since 7² + 24² equals 25², the triangle is a right triangle.
Step 8: Use the formula for the area of a right triangle: Area = (1/2) * base * height.
Step 9: Choose the base as 7 cm and the height as 24 cm.
Step 10: Calculate the area: Area = (1/2) * 7 * 24.
Step 11: Calculate (1/2) * 7 = 3.5.
Step 12: Multiply 3.5 by 24 to get the area: 3.5 * 24 = 84 cm².

Right Triangle Identification – The question tests the ability to recognize a right triangle using the Pythagorean theorem.
Area Calculation – The question assesses the understanding of how to calculate the area of a triangle using the formula for right triangles.