the area of a triangle is 150cm2 and its sides are in the ratio3:4:5. what is its perimeter
Answers
We can solve this using Heron's Formula:
We're given that the sides are in ratio 3:4:5
So, a = 3x, b = 4x, c = 5x
s = (a+b+c)/2
s = (3x+4x+5x)/2
s = 12x/2
s = 6x
Now, applying heron's formula:
150 = √6x(6x-3x)(6x-4x)(6x-5x)
150 = √6x(3x)(2x)(1x)
150 = √36x⁴
150 = 6x²
x² = 150/6
x² = 25
x = √25
x = 5
Now, we can put this value in our ratio.
a = 3x = 3(5) = 15
b = 4x = 4(5) = 20
c = 5x = 5(5) = 25
Finally, perimeter = a + b + c
= 15+20+25
= 60 cm.
The perimter of the triangle is 60cm
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Answer:
60 cm
Step-by-step explanation:
a = 3x, b = 4x, c = 5x
s = (a+b+c)/2
s = (3x+4x+5x)/2
s = 12x/2
s = 6x
Now, by heron's formula:
150 = √6x(6x-3x)(6x-4x)(6x-5x)
150 = √6x(3x)(2x)(1x)
150 = √36x⁴
150 = 6x²
x² = 150/6
x² = 25
x = √25
x = 5
Now, we can put this value in our ratio.
a = 3x = 3(5) = 15
b = 4x = 4(5) = 20
c = 5x = 5(5) = 25
Finally, perimeter = a + b + c
= 15+20+25
= 60 cm.
The perimeter of the triangle is 60cm
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