Question

the sides of a triangle are in the ratio 13 is to 14 is to 15 and its perimeter is 84 cm find the area of the triangle

Answer 1

Let a=13x,b=14x,c=15x
a+b+c=84
13x+14x+15x=84⇒42x=84⇒x=2
a=13×2=26 cm,b=14×2=28 cm,c=15×2=30 cm
s=p/2=42 cm
Area of the Δ=√s(s-a)(s-b)(s-c)
=√42×(42-26)×(42-28)×(42-30) cm²
=√42×16×14×12 cm²=√2×3×7×4×4×7×2×2×3×2 cm²
√2×2×2×2×3×3×7×7×4×4 cm²
=2×2×3×7×4 cm²=336 cm²

Answer 2

$let \: a = 13x \\ \: \: \: \: \: \: \: b = 14x \\ \: \: \: \: \: \: \: c = 15x \\ perimeter = 84 \\ \: \: \: \: a + b + c = 84 \\ 13x + 14x + 15x = 84 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 42x = 84 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{84}{42} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\: \: \: \: \: \: \: \: x = 2cm \\ a = 13 x = 26cm \\ b = 14x = 28cm \\ c = 15x = 30cm \\ s = \frac{p}{2} = \frac{84cm}{2} = 42cm \\ area \: of \: traingle \\ \sqrt {42cm \times 16cm\times 14 cm\times 12cm} \\ = = {336cm}^{2}$
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