Question

The perimeter of a triangle is \(10\) cm. If one of its sides is \(4\) cm, then the remaining sides of the triangle, when the area of the triangle is maximum, are

• A. \(5\text{ cm}, 1\text{ cm}\)
• B. \(3.6\text{ cm}, 2.4\text{ cm}\)
• C. \(3\text{ cm}, 3\text{ cm}\)
• D. \(2\text{ cm}, 4\text{ cm}\)

Hint:

For fixed perimeter problems, symmetry usually gives the maximum area condition.

Answer 1

The Correct Option is C

Step 1: Use the perimeter condition.
Let the remaining sides be \(x\) and \(y\). Then \[ 4 + x + y = 10 \Rightarrow x + y = 6 \]
Step 2: Apply the maximum area condition.
For a fixed perimeter, the area of a triangle is maximum when the remaining sides are equal.

Step 3: Final result.
\[ x = y = 3\text{ cm} \]