In triangle PQR, if PQ = 10 cm, PR = 24 cm, and QR = 26 cm, what is the area of

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Question: In triangle PQR, if PQ = 10 cm, PR = 24 cm, and QR = 26 cm, what is the area of the triangle? (2019)

Options:

Correct Answer: 120 cm²

Exam Year: 2019

Solution:

Using Heron\'s formula, s = (10 + 24 + 26) / 2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = √(4800) = 120 cm².

In triangle PQR, if PQ = 10 cm, PR = 24 cm, and QR = 26 cm, what is the area of the triangle? (2019)

In triangle PQR, if PQ = 10 cm, PR = 24 cm, and QR = 26 cm, what is the area of the triangle? (2019)

Step 1: Identify the lengths of the sides of triangle PQR. They are PQ = 10 cm, PR = 24 cm, and QR = 26 cm.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (PQ + PR + QR) / 2.
Step 3: Substitute the values into the formula: s = (10 + 24 + 26) / 2 = 30 cm.
Step 4: Use Heron's formula to find the area of the triangle. The formula is Area = √(s * (s - PQ) * (s - PR) * (s - QR)).
Step 5: Substitute the values into Heron's formula: Area = √(30 * (30 - 10) * (30 - 24) * (30 - 26)).
Step 6: Simplify the expression: Area = √(30 * 20 * 6 * 4).
Step 7: Calculate the product: 30 * 20 = 600, then 600 * 6 = 3600, and finally 3600 * 4 = 14400.
Step 8: Find the square root of 14400: Area = √(14400) = 120 cm².

Heron's Formula – A method to calculate the area of a triangle when the lengths of all three sides are known.
Semi-perimeter – The semi-perimeter (s) is half the sum of the triangle's side lengths, used in Heron's formula.
Square Root Calculation – Understanding how to compute the square root of a product to find the area.