Question

sides of the traingle are in the ratio 10 : 9 : 8 : and it's perimeter is 270m . find it's area.​

Answer 1

Step-by-step explanation:

10x+9x+8x=270

27x=270

x=270/27

x=10

Area is 10*10*10

Area=1000 m*m

Answer 2

Answer:

Given:-

sides are in ratio 10:9:8

perimeter= 270m

Let the sides of the triangle be

10x,9x,8x respectively

we know perimeter of a closed polygon=sum of all it's sides.

that is

10x+9x+8x=270

27x=270

x=270/27

x=10

therefore the angles are

10x=10×10=100

9x=9×10=90

8x=8×10=80

Let's check whether it's correct or not

10x+9x+8x=270

100+90+80=270

270=270

L.H.S=R.H.S

hence verified

and now we have to find it's area

from the sides we found

it's sure that , it's a scalene triangle

that is all 3 sides are different

So for finding the area of this triangle

we've to use Heron's Formula

that is

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

where

s=semi perimeter=perimeter/2

here perimeter=270

270/2=135

therefore the equation is

$\sqrt{(135)(135 - 100)(135 - 90)(135 - 80)} \\ = \sqrt{135 \times 35 \times 45 \times 55}$

$\sqrt{(5 \times 3 \times 3 \times 3)(5 \times 7)(5 \times 3 \times 3)(5 \times 11)}$

$5 \times 3 \times 3 \times 5 \sqrt{7 \times 3 \times 11} \\ = 225 \sqrt{231}$

therefore the correct answer is 225√231

hope it helps