Question

The sides of a triangle are 9cm, 40cm and 41cm. The area of the triangle is

• A. 180 sq.cm
• B. 184 sq.cm
• C. 190 sq.cm
• D. 240 sq.cm

Hint:

Familiarity with standard Pythagorean triplets is a major shortcut in exams.
Common triplets include \((3, 4, 5)\), \((5, 12, 13)\), \((8, 15, 17)\), and \((9, 40, 41)\).
Identifying the triplet immediately avoids the complex calculations of Heron's formula.

Answer 1

The Correct Option is A

Step 1: Check if the triangle is right-angled.
Verify using the Pythagorean theorem: 9^2 + 40^2 = 81 + 1600 = 1681 = 41^2. Yes, it is a right triangle with hypotenuse 41 cm.
Step 2: Calculate the area.
For a right triangle, the two legs serve as base and height. Area = (1/2) x 9 x 40 = 180 sq. cm.
Step 3: Confirm the result.
Since the right angle is between sides 9 and 40, the area calculation is straightforward and gives 180 sq. cm.
\[ \boxed{180} \]