construct the triangle having its perimeter 12.5cm and ratio of angles 3:4:5 .
Consider a triangle ABC whose perimeter i.e. AB + BC + AC = 12.5 cm and ∠A: ∠B: ∠C = 3:4:5
Let ∠A = 3x, ∠B = 4x and ∠C = 5x
In ∆ABC, ∠A + ∠B + ∠C = 180° [angle sum property]
⇒3x + 4x + 5x = 180°
⇒12x = 180°
⇒ x = 15°
∴ ∠A = 3 × 15° = 45°
∠B = 4 × 15° = 60°
∠C = 5 × 15° = 75°
Therefore in ∆ABC, perimeter = 12.5 cm and ∠A = 45°, ∠B = 60° and ∠C = 75°
You know how to construct a triangle if its perimeter and its two base angles are given. The method has been mentioned on pages 194 and 195 of your NCERT text book. You may also go through the lesson 5 of this chapter in our website. Similar type of question has been given asked in question 4 of exercise 11.2 of NCERT book. You can go through its solution on our website.
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