2. The lengths 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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Answer:
Given:
Length of a Δ are in ratio 3:4:5
perimeter (p)=144 cm
Also given, to find the area of Δ
⇔3x+4x+5x=144
12x=144⇔x=12
so we get
3x=3(12)=36;4(19)=48;54=5(12)=60
∴ s= 1/2(a+b+c)
= 1/2 (36+48+60)
= 1 /2 ×144⇔72 cm
Area of Δ with sides = √s(s−a)(s−b)(s−c)
= √72(72−36)(72−48)(72−60)
= √72(36)(24)(12)
=√ 2² ×3 ²×2×2 ² ×3 ²×2 ²×2×3×2 ² ×3
=√2×3×2×3×2×2×3×2
Area of Δ =864 sq.cm
HOPE IT HELP YOU..
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