A triangle has side lengths x\text{ cm}, x+13\text{ cm} and x+26\text{ cm}. If its area is 126 square cm, then what is the value of x ?

Explanation

Testing option 15, the sides are 15, 28, 41. Semi-perimeter s = \frac{15+28+41}{2} = 42. By Heron's formula, Area = \sqrt{42(42-15)(42-28)(42-41)} = \sqrt{42 \times 27 \times 14 \times 1} = \sqrt{15876} = 126\text{ cm}^2, confirming x = 15.

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