Question

find the area of triangle whose sides are in ratio 4:5:6 and perimeter is 300 ..pls ans it fast​

Answer 1

ɢɪᴠᴇɴ

• Perimeter of triangle = 300
• Sides = 4x, 5x and 6x

ᴛᴏ ғɪɴᴅ

• Area of triangle.

ʟᴇᴛ, ᴛʜᴇ ʀᴀᴛɪᴏs ʙᴇ ᴛʜᴇ ᴍᴜʟᴛɪᴘʟᴇ ᴏғ x.

sᴏ, ᴅɪᴍᴇɴsɪᴏɴs ᴡɪʟʟ ʙᴇ

• 4x , 5x and 6 x

FORMULA

1. $\bold{Perimeter =side+side+side}$

2.$\bold{Area =\sqrt{s(s-a)(s-b)(s-c)}}$

NOW

$\bold{Perimeter =side+side+side}$

$=> 300 = 4x +5x +6x$

$=> 300 = 15x$

$=>\frac{300}{15} =x$

$=> 20 = x$

ᴅɪᴍᴇɴsɪᴏɴs

• 4x = 4×20 =80 __(a)
• 5x = 5×20 =100 __(b)
• 6x = 6×20 = 120 __(c)

ɴᴏᴡ

$\large\bold{s = \frac{a+b+c}{2}}$

$\large\bold{s = \frac{80+100+120}{2}}$

$\large\bold{s = \frac{300}{2}}$

$\large\bold{s = 150}$

ʙʏ ᴜsɪɴɢ ʜᴇʀᴏɴ's ғᴏʀᴍᴜʟᴀ

$\bold{Area =\sqrt{s(s-a)(s-b)(s-c)}}$

$A = \sqrt{s(s-a)(s-b)(s-c)}$

$A =\sqrt{150(150-80)(150-100)(150-120)}$

$A =\sqrt{150×70×50×30}$

$A =\sqrt{15750000}$

$A =3968.6$

ᴛʜᴇʀᴇғᴏʀᴇ

AREA = 3968.6

HOPE THIS ANSWER WILL HELP YOU!!

Answer 2

Given :

• Sides are in ratio 4:5:6
• Perimeter is 300

To find :

• Area of triangIe

SoLution :

As sides are in ratio of 4:5:6 .

Let the sides be 4x, 5x, 6x units.

Now we know that :

⇒ Perimeter of Δ = Sum of 3 sides of Δ

ATQ,

⇒ 4x + 5x + 6x = 300

⇒ 15x = 300

⇒ x = 300/15

⇒ x = 20 units.

Now finding sides of Δ :

1. 4x = 4 × 20 =  80 units.
2. 5x = 5 × 20 = 100 units.
3. 6x = 6 × 20 = 120 units.

Now using Heron's formuLa :

⇒ Area of Δ = √[s(s - a)(s - b)(s - c)]

Where, s = semi perimeter

⇒ s = 300/2

⇒ s = 150 units.

Substituting  :

⇒ Area of Δ = √[150(150 - 80)(150 - 100)(150 - 120)]

⇒ Area of Δ = √[150 × 70 × 50 × 30]

⇒ Area of Δ = √15750000

⇒ Area of Δ = 3968.63 unit²

∴ Area of Δ = 3968.63 unit²