The perimeter of an isosceles triangle is 20cm and it's unequal side is 5cm, then find its area.
Answers
Step-by-step explanation:
Given:-
The perimeter of an isosceles triangle is 20cm and it's unequal side is 5cm.
To find :-
Find its area.?
Solution :-
Let the equal sides of an Isosceles triangle be a units each.
The length of unequal side of the Isosceles triangle (b) = 5 cm
We know that
The perimeter of an Isosceles triangle
= 2a+b units
Where, a = length of the equal sides
and b = length of the unequal side
=> Perimeter of the Isosceles triangle
=> P = 2a+5 cm
According to the given problem
The perimeter of an isosceles triangle = 20 cm
=> 2a+5 = 20
=> 2a = 20-5
=> 2a = 15
=> a = 15/2
=> a = 7.5 cm
The length of the equal side each = 7.5 cm
We know that
Area of an Isosceles triangle = (b/4)√(4a²-b²) sq.units
=> Area = (5/4)√[4(7.5)²-5²]
=> Area = (5/4)√[4(56.25)-25]
=> Area = (5/4)√(225-25)
=> Area = (5/4)√200
=> Area = (5/4)√(2×100)
=> Area = (5/4)×10√2
=> Area = (50/4)√2
=> Area = (25/2)√2 sq.cm or
=> Area = (25/2)(1.414) sq.cm
=> Area = 17.675 sq.cm
Answer:-
The area of the given Isosceles triangle is
(25√2)/2 sq.cm or 17.675 sq.cm
Used formulae:-
→ Area of an Isosceles triangle = (b/4)√(4a²-b²) sq.units
→ The perimeter of an Isosceles triangle
= 2a+b units
Where, a = length of the equal sides
and b = length of the unequal side