I-have-a-loop-of-string-of-length-perimeter-p-units-I-want-to-make-a-triangle-of-largest-area-from-the-loop-What-will-be-the-dimensions-of-that-triangle-

Question Number 1592 by Rasheed Soomro last updated on 23/Aug/15

I have a loop of string of length (perimeter) p units .

I want to make a triangle of largest area from the

loop . What will be the dimensions of that triangle ?

Commented by 123456 last updated on 23/Aug/15

x + y + z = p

s = p / 2

{\begin{cases} ∣ x - y ∣⩽ z ⩽ x + y \\ ∣ x - z ∣⩽ y ⩽ x + z \\ ∣ y - z ∣⩽ x ⩽ y + z \end{cases}

S (x, y, z) = \sqrt{s (s - x) (s - y) (s - z)}

Answered by prakash jain last updated on 10/Dec/15

x = y = z = \frac{p}{3}

among all triangle of same perimeter

equilateral triangle has largest area .