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

₹0.0

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

Options:

Correct Answer: 120 cm²

Solution:

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

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

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

Step 1: Identify the lengths of the sides of triangle PQR. We have PQ = 10 cm, QR = 24 cm, and PR = 26 cm.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (PQ + QR + PR) / 2.
Step 3: Substitute the values into the formula: s = (10 + 24 + 26) / 2.
Step 4: Add the lengths: 10 + 24 + 26 = 60.
Step 5: Divide by 2 to find s: s = 60 / 2 = 30 cm.
Step 6: Use Heron's formula to find the area of the triangle: Area = √(s * (s - PQ) * (s - QR) * (s - PR)).
Step 7: Substitute the values into Heron's formula: Area = √(30 * (30 - 10) * (30 - 24) * (30 - 26)).
Step 8: Calculate each term: (30 - 10) = 20, (30 - 24) = 6, (30 - 26) = 4.
Step 9: Now substitute these values: Area = √(30 * 20 * 6 * 4).
Step 10: Calculate the product: 30 * 20 = 600, then 600 * 6 = 3600, and finally 3600 * 4 = 14400.
Step 11: Take the square root of 14400 to find the area: 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.
Triangle Inequality Theorem – A principle that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.