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Set up equations based on the properties of an equilateral triangle.

Mathematics

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For Fig. 7.1, it is assumed that the third side is (a+b+2)(a+b+2) cm, interpreting 'c' as '2' to allow for numerical solutions.

Step 1: Set up equations based on the properties of an equilateral triangle.
In an equilateral triangle, all sides are equal.

4a=3b(1)4a = 3b \quad (1) 4a=a+b+2(2)4a = a+b+2 \quad (2)

Step 2: Solve the system of equations for aa and bb.
From equation (2):

4a−a=b+24a - a = b+2 3a=b+23a = b+2 b=3a−2(3)b = 3a-2 \quad (3)

Substitute equation (3) into equation (1):

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