The ratio of the measure of side of triangle is 3:4:5 8its perimeter 72 cm find the area of the triangle
Answers
☀️ Answer: Area of the triangle is 216cm²
Given that: Ratio of measure of sides of triangle is 3:4:5.
Perimeter of triangle is 72cm
Need to find: Area of that triangle
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❍ To calculate the area of the triangle we must know that ::
⚝ Perimeter of a triangle = a + b + c
⚝ Area of a triangle = ½ × base × height
Where,
- a, b and c denotes sides of the triangle
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~ Let's say that sides of the triangle are 3x, 4x and 5x according to the given ratios.
- a = 3x
- b = 4x
- c = 5x
T H E R E F O R E,
⇢ a + b + c = 72
⇢ 3x + 4x + 5x = 72
⇢ 12x = 72
⇢ x = 72/12
⇢ x = 6
Finding the sides :-
- a = 3x = 3 × 6 = 18cm
- b = 4x = 4 × 6 = 24cm
- c = 5x = 5 × 6 = 30cm
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~ Here, we can clearly see that it is a right angled triangle :
{ According to Pythagoras Theorem }
→ [ 30 ]² = [ 18 ]² + [ 24 ]²
→ 900 = 324 + 576
→ 900 = 900
Here,
- 30cm is Hypotenuse
- 18 and 24 are base and height
Finding the area of triangle :-
⇢ ½ × 24 × 18
⇢ 12 × 18
⇢ 216cm²
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- Henceforth, Area of the triangle is 216cm²