Question

Q1 Find the perimeter of equilateral triangle whose area is 600 meter square
Q2 let triangle be the area of area of triangle . find the area of traiangle whose each side is twice the side of given triangle

Answer 1

Solution 1)

Given that area of equilateral triangle is 600 m².

Area of equilateral triangle = √3/4 (side)²

Let side = a

→ 600 = √3/4 a²

→ 600 × 4 = √3 a²

→ a² = 2400/√3

→ a² = 800√3

→ a = 20√6

Now,

Perimeter of triangle = 3 × side

From above calculations side (a) = 20√6

→ Perimeter = 3 × 20√6

→ Perimeter = 60√6

•°• Perimeter of triangle is 60√6 m

______________________________

Solution 2)

Let sides of traingle be a, b and c.

Semi-perimeter (s) = (a + b + c)/2

Now,

By Heron's formula :

s = √[s (s - a) (s - b) (s - c)]

Let √[s (s - a) (s - b) (s - c)] = M __ (eq 1)

From above, s = (a + b + c)/2

According to question,

If sides are doubled then,

New sides = 2a, 2b and 2c.

And s bcomes 2s.

Then,

Area = √[s (s - a) (s - b) (s - c)]

=> √[2s (2s - 2a) (2s - 2b) (2s - 2c)]

=> √[2s 2(s - a) 2(s - b) 2(s - c)]

=> √[16s (s - a)(s - b)(s - c)]

=> 4√[s (s - a)(s - b)(s - c)

So, 2s = 4M [From (eq 1)]

•°• Area of traingle is 4 times the area of triangle whose each side is twice the side of given triangle.

Answer 2

Answer:

Step-by-step explanation:

Answer 2

Given :-

Triangle be the area of area of triangle.

Each side is twice the side of given triangle.

To Find :-

Area of triangle.

Solution :-

Let all sides be a, b, and c.

According to the question,

Sides = 2a, 2b and 2c

⇒ Area = √s(s-a)(s-b)(s-c)

⇒ Area  = √2s(2s-2a)(2s-2b)(2s-2c)

⇒ Area  = √2s 2(s-a) 2(s-b) 2(s-c)

⇒ Area  = √16s(s-a)(s-b)(s-c)

⇒ Area  = 4√s(s-a)(s-b)(s-c)

⇒ Area  = 4x

Hence, the area of traiangle 4x.