In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area

₹0.0

Question: In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?

Options:

Correct Answer: 60

Solution:

Using Heron\'s formula, the semi-perimeter s = (8 + 15 + 17)/2 = 20. Area = √[s(s-a)(s-b)(s-c)] = √[20(20-8)(20-15)(20-17)] = √[20*12*5*3] = 60.

In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?

In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?

Step 1: Identify the lengths of the sides of the triangle. Here, side a = 8, side b = 15, and side c = 17.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (a + b + c) / 2. So, s = (8 + 15 + 17) / 2 = 20.
Step 3: Use Heron's formula to find the area of the triangle. The formula is Area = √[s(s-a)(s-b)(s-c)].
Step 4: Substitute the values into the formula. We have Area = √[20(20-8)(20-15)(20-17)].
Step 5: Calculate each term inside the square root: (20-8) = 12, (20-15) = 5, (20-17) = 3.
Step 6: Now substitute these values back into the formula: Area = √[20 * 12 * 5 * 3].
Step 7: Calculate the product: 20 * 12 = 240, then 240 * 5 = 1200, and finally 1200 * 3 = 3600.
Step 8: Take the square root of 3600 to find the area: √3600 = 60.

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.