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.

Question

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. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For maximum value of perimeter of triangle AEB , λ=(1/2) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2bb038c528ceeb9302e451727462bf28-.png" /> ∴ Perimeter =2 √(1/4)+1+1=√5+1

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

For maximum value of perimeter of $△ A EB, λ = \frac{1}{2}$

$∴$ Perimeter $= 2 \frac{1}{4} + 1 + 1 = 5 + 1$

Q. Let ABCD be a square of side 1 unit. A triangle ABE is formed where E is any point on side CD. If the greatest possible value of perimeter of triangle ABE is 1+n​, where n∈N, then find the value of n.

For maximum value of perimeter of △AEB,λ=21​ ∴ Perimeter =241​+1​+1=5​+1

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

For maximum value of perimeter of $△ A EB, λ = \frac{1}{2}$

$∴$ Perimeter $= 2 \frac{1}{4} + 1 + 1 = 5 + 1$