1. Tardigrade
  2. Question
  3. Mathematics
  4. Let ABCD be a square of side 1 unit. A triangle ABE is formed where E is any point on side C D. If the greatest possible value of perimeter of triangle A B E is 1+√n, where n ∈ N, then find the value of n.

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Q. Let $ABCD$ be a square of side 1 unit. A triangle $ABE$ is formed where $E$ is any point on side $C D$. If the greatest possible value of perimeter of triangle $A B E$ is $1+\sqrt{n}$, where $n \in N$, then find the value of $n$.

Application of Derivatives

Solution:

For maximum value of perimeter of $\triangle AEB , \lambda=\frac{1}{2}$
image
$\therefore$ Perimeter $=2 \sqrt{\frac{1}{4}+1}+1=\sqrt{5}+1$