The sides of a triangle are in the ratio 3 : 4 : 5. If perimeter of the
triangle in 360m, find its area using Heron’s formula.
Answers
Answer:
area of a triangle is 5400m2
Step-by-step explanation:
side s of a triangle= 3:4:5.
perimeter of a triangle= 360m
area of a triangle is
let it be =3x,4x,5x
perimeter of a triangle=a+b+c
3x+4x+5x= 360m
12x = 360m
x= 360/12
x=30
sides of triangle
3x= 3x3o= 90
4x=4x30= 120
5x=5x30=150
Area of triangle using heron's method
area of triangle= √s(s-a)(s-b)(s-c)
S= semi perimeter=perimeter/2
360/2=180
S=180
area of triangle
√180(180-90)(180-60)(180-30)
≤√180x90x30. =√2916000
the root of √21960000=5400
hence area of triangle is =5400m2.....!!!!!!!
Step-by-step explanation:
Area of triangle is 5400 m².
Step-by-step explanation:
Given:-
Sides of triangle are in ratio 3:4:5.
Perimeter of triangle is 360 m.
To find:-
Area of triangle.
Solution:-
Let, Sides of triangle be 3x, 4x and 5x.
Perimeter of triangle = a+b+c
Where, a,b and c are sides of triangle.
Puting sides and perimeter of triangle.
\longrightarrow ⟶ 3x + 4x + 5x = 360
\longrightarrow ⟶ 12x = 360
\longrightarrow ⟶ x = 360/12
\longrightarrow ⟶ x = 30
Sides of triangle :-
3x = 3×30 = 90
4x = 4×30 = 120
5x = 5×30 = 150
Sides of triangle are 90m, 120m and 150m.
Area of triangle by using Heron's formula is :
Area of triangle = \bold{\sqrt{s(s-a)(s-b)(s-c)}}
s(s−a)(s−b)(s−c)
Where,
S is semi-perimeter of triangle.
a, b and c are sides of triangle.
So,
Semi-perimeter = Perimeter/2
= 360/2
= 180
Semi-perimeter of triangle is 180 m.
Area of triangle:
\longrightarrow ⟶ √180(180 - 90)(180 - 60)(180 - 30)
\longrightarrow ⟶ √180 × 90 × 60 × 30
\longrightarrow ⟶ √29160000
\longrightarrow \purple{\boxed{\sf \bold{ 5400}} \star} ⟶
5400
⋆
Therefore,
Area of triangle is 5400 m².