if the ratio of sides is 25:14:12 and the perimeter is 510. the area is 4449.08. True/False
Answers
Answer:
True
Step-by-step explanation:
Given :-
The ratio of sides is 25:14:12 and the perimeter is 510 of a triangle
To find :-
The area is 4449.08. True/False?
Solution :-
Given that
The ratio of sides is 25:14:12
Let they be 25X , 14X and 12X
We know that
Perimeter of a triangle = Sum of the lengths of the sides
=> P = 25X+14X+12X
=> P = 51X
According to the given problem
Perimeter of a triangle = 510
=> 51X = 510
=> X = 510/51
=> X = 10
The value of 25X = 25×10 = 250
The value of 14X = 14×10 = 140
The value of 12X = 12×10 = 120
We have
a = 250 units
b = 140 units
c = 120 units
The area of a triangle by Heron's formula
=>√[S(S-a)(S-b)(S-c)] sq.units
Where, S = (a+b+c)/2 units
=> S = (250+140+120)/2
=> S = 510/2
=> S = 255 units
Now,
Area = √[255(255-250)(255-140)(255-120)]
=> Area =√(255×5×115×135)
=> Area =√ 19794375
=> Area = 4449.08 sq.units
Answer:-
Area of the given triangle is 4449.08 sq.units
It's true
Used formulae:-
→Perimeter of a triangle = Sum of the lengths of the sides
→ The area of a triangle by Heron's formula
=√[S(S-a)(S-b)(S-c)] sq.units
→ Where, S = (a+b+c)/2 units
→ a,b,c are the three sides