2022 · Q95
A triangle has side lengths x cm, x + 13 cm and x + 26 cm. If its area is 126 square cm, then what is the value of x?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A18
- B17
- C16
- D15
Explanation
Trying x = 15: sides 15, 28, 41 with s = 42; Heron gives √(42·27×14×1) = √15876 = 126, as required. With sides in arithmetic progression, trying integer x against Heron's formula is the fastest route. The keyed option is D.