find the area of a triangle two sides of which are 18cm and 10cm and perimeter 42 cm
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Answered by
8
Given sides
a = 18
b = 10
_______________
Perimeter = a+b+c
42 = 18+10+c
c = 14
_______________
S = (a+b+c)/2
= 21
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Using Heron's formula Area of triangle is
= root (s)×(s-a)×(s-b)×(s-c)
= root (21)×(21-18)×(21-10)×(21-14)
= root (21×3×11×7)
= root (21×21×11)
Area = 21√11 units
_________________
a = 18
b = 10
_______________
Perimeter = a+b+c
42 = 18+10+c
c = 14
_______________
S = (a+b+c)/2
= 21
=================
Using Heron's formula Area of triangle is
= root (s)×(s-a)×(s-b)×(s-c)
= root (21)×(21-18)×(21-10)×(21-14)
= root (21×3×11×7)
= root (21×21×11)
Area = 21√11 units
_________________
Answered by
2
Question:
- Find the area of a triangle two sides of which are 18cm and 10cm and perimeter 42 cm.
Answer:
- Therefore, the area of the triangle is 21√11 cm².
Step-by-Step Explanation:
Given:
- Two sides of the ∆ are 18 cm and 10 cm & the perimeter is 42 cm.
To find:
- Area of the triangle
Solution:
Let's Consider, the third side be x cm.
★ Perimeter of ∆ = (a + b + c)
➟ 18 + 10 + x = 42
➟ 28 + x = 42
➟ x = 42 – 28
➟ x = 14
- The third side of the triangle is 14 cm.
If the perimeter of the triangle is 42 cm then semi perimeter of the triangle would be 21 cm. i.e ( s ) = 21 cm.
Using Heron's Formula :
➟ ⠀Ar. = √(s – a) (s – b) (s – c)
➟ ⠀Ar. = √(21 – 18) (21 – 10) (21 – 14)
➟ ⠀Ar. = √7 × 3 × 3 × 11 × 7
➟ ⠀Ar. = 7 × 3√11
➟ ⠀Ar. = 21√11
Therefore, the area of the triangle is 21√11 cm².
_____________________________
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