Heron’s formula – Triangle with sides 13 cm, 14 cm, 15 cm: Find the exact area (in square centimetres) of a triangle whose side lengths are 13 cm, 14 cm, and 15 cm.
Aptitude
Area
Difficulty: Easy
Choose an option
-
A84
-
B64
-
C44
-
D22
-
ENone of these
Answer
Correct Answer: 84
Explanation
Introduction / Context:For a triangle given by three sides, use Heron’s formula: Area = √(s(s − a)(s − b)(s − c)), where s is the semiperimeter.
Given Data / Assumptions:
- a = 13 cm, b = 14 cm, c = 15 cm.
- All sides satisfy the triangle inequality.
Concept / Approach:Compute s, then apply Heron’s formula carefully without rounding until the end to keep it exact.
Step-by-Step Solution:
s = (13 + 14 + 15) / 2 = 42 / 2 = 21.Area = √(21 * (21 − 13) * (21 − 14) * (21 − 15))= √(21 * 8 * 7 * 6) = √(21 * 336) = √(7056) = 84 sq cm.Verification / Alternative check:13-14-15 is a classic Heron triple yielding area 84; many exam keys list this as a standard exact value.
Why Other Options Are Wrong:64, 44, 22 are not consistent with Heron’s calculation for these sides.
Common Pitfalls:Arithmetic slips in semiperimeter or inside the square root; premature rounding.
Final Answer:84