The lengths of the sides of a triangle are in the ratio 4 : 5 : 3 and its perimeter is 192 cm. Find its area.
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The lengths of the sides of a triangle are in the ratio 4 : 5 : 3 and its perimeter is 192 cm. Find its area.
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Given :
To find :
Knowledge required ::
⠀⠀⠀Perimeter = sum of all sides
[where : a, b and c are the three sides of the triangle.]
or
Solution :
Let the three sides of the triangle be 4x, 5x and 3x.
⠀⇒ Perimeter = Sum of all sides
⠀⠀⠀⠀⠀⠀⇒ 192 = 4x + 5x + 3x
⠀⠀⠀⠀⠀⠀⇒ 192 = 12x
⠀⠀⠀⠀⠀⠀⇒ 192/12 = x
⠀⠀⠀⠀⠀⠀⇒ 96/6 = x
⠀⠀⠀⠀⠀⠀⇒ 48/3 = x
⠀⠀⠀⠀⠀⠀⇒ 16 = x
The value of x = 16
• Substitute the value of x in the sides which we have let.
⠀⠀⠀⠀⠀⠀⇒ 4x = 4 × 16 = 64
⠀⠀⠀⠀⠀⠀⇒ 5x = 5 × 16 = 80
⠀⠀⠀⠀⠀⠀⇒ 3x = 3 × 16 = 48
⠀⠀⠀⠀⠀⠀⇒ s = 192/2
⠀⠀⠀⠀⠀⠀⇒ s = 96
Semi - perimeter of the triangle = 96 cm
Take,
⇒ Area = √s(s - a)(s - b)(s - c)
⇒ Area = √96(96 - 64)(96 - 80)(96 - 48)
⇒ Area = √96(32)(16)(48)
⇒ Area = 1536
★ Area of the triangle = 1536 cm²
Verified answer
Step-by-step explanation:
perimeter of triangle =side +side+side
192=4x+5x+3x
192=12x
x=16