In triangle ABC, the length of side BC is 2 cm less than twice the length of side AB. The length of side AC exceeds the length of side AB by 10 cm. The perimeter of the triangle is 40 cm. Determine the length (in cm) of the smallest side of the triangle.

Question

Accepted Answer

Let the length of side AB be x cm.

Given:
- BC = 2x - 2 cm (2 cm less than twice AB)
- AC = x + 10 cm (10 cm more than AB)
- Perimeter = AB + BC + AC = 40 cm

Form the equation:

x + (2x - 2) + (x + 10) = 40

Simplify:
4x + 8 = 40
4x = 32
x = 8

So, AB = 8 cm
BC = 2(8) - 2 = 16 - 2 = 14 cm
AC = 8 + 10 = 18 cm

The smallest side is AB = 8 cm.

Answer

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