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Question
Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55 m.
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Solution
Let the third side of triangle be x m.
Then, two equal sides of triangle = (3x – 4) m
Given, perimeter of triangle = 55 m
∵ Perimeter of a triangle = Sum of the sides of the triangle
∴ x + 3x – 4 + 3x – 4 = 55
⇒ 7x – 8 = 55
⇒ 7x = 55 + 8
⇒ 7x = 63
⇒ x = `63/7`
∴ x = 9
Hence, the dimensions of the triangle are 9 m, (3 × 9 – 4) m and (3 × 9 – 4) m, i.e. 9, (27 – 4) and (27 – 4) m, i.e. 9 m, 23 m and 23 m.
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