The perimeter of a triangle is 12m . Find the maximum area if sides are in natural no.
Answers
Step-by-step explanation:
3a=12
a=12/3
a=4cm
each side is 4cm
The maximum area of triangle would be 4√3 m²
The given perimeter of the triangle is 12 m
The sides are given as natural numbers.
Also, the length of a side of triangle is always greater than the difference in length of other two sides and less than the sum of lengths.
The possible combinations for length would be
1) 2,5,5
2) 3,4,5
3) 4,4,4
The first one is an isosceles triangle, so its area would be
A = ½[√(a^2 − b^2 ⁄4) × b] where a is the length of equal sides
Hence, area would be
A = ½[√(5^2 − 2^2 ⁄4) × 2] = ½[√(25 − 1) × 2]
= 1/2 * √48 = 1/2 * 4√3 = 2√3 m²
Second, triangle is a right angle triangle since, the lengths form a pythagorean triplet
Hence area would be 1/2 * B*H = 1/2 * 3*4 = 6 m²
Third triangle is an equilateral triangle hence area would be
1/4 * √3 * a² = 4√3 m²