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Find the semi- perimeter of triangle whose sides ar 6 cm cm 7 cm \& 9 cm

Ask by Long Ryan. in India
Jan 23,2025

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Answer

The semi-perimeter of the triangle is 11 cm.

Solution

To find the **semi-perimeter** of a triangle, you can use the following formula: \[ \text{Semi-perimeter} (s) = \frac{a + b + c}{2} \] Where: - \( a \), \( b \), and \( c \) are the lengths of the sides of the triangle. Given the sides of the triangle: - \( a = 6 \) cm - \( b = 7 \) cm - \( c = 9 \) cm **Step-by-Step Calculation:** 1. **Add all three sides together:** \[ 6\ \text{cm} + 7\ \text{cm} + 9\ \text{cm} = 22\ \text{cm} \] 2. **Divide the sum by 2 to find the semi-perimeter:** \[ s = \frac{22\ \text{cm}}{2} = 11\ \text{cm} \] **Conclusion:** The semi-perimeter of the triangle is **11 cm**.

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To find the semi-perimeter of a triangle, you add the lengths of all three sides and then divide by 2. In this case, the sides are 6 cm, 7 cm, and 9 cm. So, the semi-perimeter \(s\) is calculated as: \[ s = \frac{6 + 7 + 9}{2} = \frac{22}{2} = 11 \text{ cm} \] Therefore, the semi-perimeter of the triangle is 11 cm. Did you know that the semi-perimeter is often used in Heron's formula? This formula allows you to calculate the area of a triangle when you know the lengths of all three sides, just using the semi-perimeter and those lengths! Triangles have been a part of mathematics for over 4,000 years! Ancient Egyptians used triangular shapes in their architectural designs, like the pyramids, and Pythagoras famously studied right triangles. The study of triangles has led to significant advancements in geometry and trigonometry, making them fundamental to many fields today!

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