Question

a rope of length 12m is given. Find the largest area of s triangle firmed by this rope and find the dimensions of the triangle so formed

Answer 1

Answer:

the largest traingle can be formed by the rope will be the equilateral traingle

therefore sides of traingle =12/3=4m=a

area of traingle = a^2√3/4 = 4^2√3/4=4√3 sq.m

Answer 2

Given :

• Length of the rope = 12m
• Perimeter of the triangle = 12m

To Find :

• The largest triangle formed

Solution :

The equilateral triangle has the maximum area for any fixed perimeter.

Let a be the side of the equilateral triangle.

⇒ a + a + a = 12

⇒ 3a = 12

⇒ a = 12 / 3

⇒ a = 14 m

Let AD be the height of the equilateral ∆ABC

⇒ AD = $\sqrt{ {AB }^{2} - \: {BD}^{2} }$

⇒ AD = $\sqrt{ {4}^{2} - {2}^{2} }$

⇒ AD = $\sqrt{16 - 4}$

⇒ AD = $\sqrt{12}$

⇒ AD = 2√3

•°• Area of the largest triangle ABC = 1/2 × BC × AD

= 1/2 × 4 × 2√3

= 4√3 sq.m

Thus, the large triangle formed is 4√3 sq.m