Question 6 - End-of-Chapter Exercises - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

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Question 6 The sides of a triangle have lengths 7" " cm,24" " cm,25" " cm. Find the area of the triangle in two different ways. Given our sides 7 cm, 24 cm, 25 cm This follows Pythagoras theorem 〖𝟐𝟓〗^𝟐=𝟕^𝟐+〖𝟐𝟒〗^𝟐 So, our triangle is a right angled triangle Let’s find Area by Herons formula Base height formula Area by Herons formula Since our sides are 7, 24, 25 ∴ a = 7, b = 24, c = 25 Now, s = (𝒂 + 𝒃 + 𝒄)/𝟐 = (7 + 24 + 25)/2 = 56/2 = 28 cm Now , Area of Triangle = √(𝑠 (𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)) = √(𝟐𝟖(𝟐𝟖−𝟕) × (𝟐𝟖−𝟐𝟒) × (𝟐𝟖−𝟐𝟓)) = √(28 × 21 × 4 × 3) = √(7 × 4 × 7 × 3 × 4 × 3) = √(7^2 × 3^2 × 4^2 ) = 7 × 3 × 4 = 7 × 12 = 84 cm2 Area by Base Height formula Since it is a right angled triangle Base = 7 cm Height = 24 cm Now, Area of triangle = 1/2 × Base × Height = 𝟏/𝟐 × 7 × 24 = 7 × 12 = 84 cm2