Question

The Perimeteres or a tiangle triangular bield
ich 144 cm and the ratio of the side is 3: 4.5
bind the area of the field.​

Answer 1

ANSWER- 864cm²

Solution-

perimeter=144cm

let the common multiple be x

the ratio of the side is 3: 4:5

3x+4x+5x=144

7x+5x=144

12x=144

x=12

hence the sides are

3x= 3×12 =36

4x= 4×12= 48

5x= 5×12=60

here,

60²=3600

48²=2304

36²=1296

48²+36²= 2304+1296= 3600

48²+36²=60²

hence the triangle is right angled triangle.

Area=½× base × height

Area=½× 48 ×36

Area= ½× 1728

Area= 864cm²


hope this helps you :-)

Answer 2

Answer:

Step-by-step explanation:

perimeter=144

ratio=3:4:5

let x be a common coefficient for all sides of the field,

∴ 3x+4x+5x=144

⇒12x=144

⇒x=144/12=12

⇒x=12

so the sides are,

• 3x=3×12=36=a
• 4x=4×12=48=b

• 5x=5×12=60=c

now by Heron's formula ,

s=144/2=72

s-a= 72-36=36

s-b=72-48=24

s-c= 72-60=12

plugging values in formula,

ar( Δ ) = √(s(s-a)(s-b)(s-c))

⇒√(72×36×24×12)

⇒864

∴ area of triangular field is 864 m².