Find the atea of a triangle two side of which are 18cm and 10cm and the perimeter is 42cm
Answers
Given :-
two of the sides of the triangle are 18cm and 10cm respectively.
let the third side be x
perimeter of the triangle is given = 42cm
we know that, sum of all sides = perimeter of the triangle
➡ 18 + 10 + x = 42cm
➡ 28 + x = 42cm
➡ x = 42 - 28
➡ x = 14
hence, the length of the third side is 14cm.
now semi-perimeter of the triangle = 42/2 = 21cm
area of the triangle by heron's formula = √[s(s - a)(s - b)(s - c)]
(s = semi-perimeter. a, b and c are the sides of the ∆)
= √[21(21 - 18)(21 - 10)(21 - 14)]
= √(21 × 3 × 11 × 7)
= √(3 × 7 × 3 × 11 × 7)
= √(3 × 3 × 7 × 7 × 11)
= 21√11cm²
hence, the area of the triangle is 21√11cm²
Answer:
The area of triangle two side of which are = 18 cm and 10 cm .
Perimeter = 42 cm
The sum of all sides = perimeter of triangle .
=18+10+x=42cm
= 28 + X = 42
x= 42 - 28
X= 14
So the third side = 14 cm
The perimeter of triangle = 42
= 42/2
= 21 cm
Heron's formula of the area of triangle
= √[ S ( S - A ) ( S - B) ( S - C)]
= [ 21( 21-18)(21-10)(21-14)]
= √(21× 3 × 11 × 7)
= √(3 × 7 × 3 × 11 × 7)
= √(3 × 3 × 7 × 7 × 11)
= 21√11cm^2