the ratio of the measures of three sides of a triangle is 4 ratio 2 ratio 3 and its perimeter is 36 cm find the area of the triangle
Answers
Given : The lengths of the sides of a triangle are in the ratio 4 : 2 : 3 and its perimeter is 36 cm.
To find : Area of the triangle
Solution:
Let the sides be a = 4x , b = 2x and c = 3x .
Perimeter of ∆ = a + b + c
⇒ 36 = 4x + 2x + 3x
⇒ 9x = 36
⇒ x = 36/9
⇒ x = 4
So , the Sides of a triangle are :
a = 4x = 4 × 4 = 16 cm
b = 2x = 2 × 4 = 8 cm
c = 3x = 3 × 4 = 12 cm
Semi Perimeter of the ∆,s = (a + b + c) /2
Semi-perimeter (s) = (16 + 8 + 12)/2
s = 36/2
s = 18 cm
Using Heron’s formula :
Area of the ∆ , A = √s (s - a) (s - b) (s - c)
A = √18(18 - 16)(18 - 8)(18 - 12)
A = √18 × 2 × 10 × 6
A = √(36 × 60)
A = √36 × 15 × 4
A = 6 × 2√15
A = 12√15
A = 12 × 3.87
A = 46.44 cm²
Hence, the area of the triangle is 46.44 cm².
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