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Question
The length of the sides of a triangle are in the ratio 3: 4: 5. Find the area of the triangle if its perimeter is 144 cm.
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Solution
Let the sides of the triangle are
a = 3x
b = 4x
c = 5x
Given that the perimeter is 144 cm.
Hence
3x + 4x + 5x = 144
⇒ 12x = 144
⇒ x = `144/12`
⇒ x = 12
s = `(a + b + c)/(2)`
= `(12x)/(2)`
= 6x
= 6 × 12
= 72
The sides are a = 36 cm, b = 48 cm and c = 60 cm.
Area of the triangle is
A = `sqrt (s(s - a )( s - b ) (s - c ))`
= `sqrt (72(72 - 36 )( 72 - 48 ) (72 - 60))`
= `sqrt (72 xx 36 xx 24 xx 12)`
= `sqrt746496`
= 864 cm2
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