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Question
The perimeter of a triangle is 14.4 cm and the ratio of lengths of its side is 2 : 3 : 4. Construct the triangle.
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Solution 1
Explanation:
Let ΔABC be the required triangle.
Draw the line XY = 14.4 cm, which is the perimeter of ΔABC.
Divide line XY in the ratio 2:3:4.
Draw ray XP such that, ∠YXP = 30°.
Draw line YQ on the opposite side of ray XP such that, `angle`XYQ = 30°.
Make ray XP into 9 equal parts i.e. `"X"_(x_1)`,x1x2, ... x8x9.
Similarly, according to the figure, make 9 equal parts of ray YQ.
Join x2y7 and x5y4, intersecting line XY at B and C respectively.
Draw an arc considering B as center and BX as radius.
Taking C as center and CY as radius, draw an arc which intersects the first arc at point A.
Draw line AB and line AC.
∴ ΔABC is the required triangle.
Solution 2
Rough figure:
Explanation:
Let the common multiple be x
∴ In ∆ABC,
AB = 2x cm, AC = 3x cm, BC = 4x cm
Perimeter of triangle = 14.4 cm
∴ AB + BC + AC = 14.4
∴ 9x = 14.4
∴ `x = 14.4/9`
∴ x = 1.6
∴ AB = 2x = 2 × 1.6 = 3.2 cm
∴ AC = 3x = 3 × 1.6 = 4.8 cm
∴ BC = 4x = 4 × 1.6 = 6.4 cm
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