Question

19The area of a triangle is 150 cm^2 and its sides are in the ratio 3 : 4 : 5. What is its perimeter?

Answer 1

Step-by-step explanation:

Let the sides to be 3x, 4x and 5x.

Semi-Perimeter of triangle = 3x+4x+5x/2 = 12x/2 = 6x

By using Hero's formula,

$area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 150 \: {cm}^{2} = \sqrt{6x(6x - 3x)(6x - 4x)(6x - 5x)} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 150 \: {cm}^{2} = \sqrt{6x \times 3x \times 2x \times x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 150 \: {cm}^{2} = \sqrt{36 {x}^{4} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 150 \: {cm}^{2} = 6 {x}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{150 \: {cm}^{2} }{6} = {x}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 25 \: {cm}^{2} = {x}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sqrt{25 \: {cm}^{2} } = x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{x = 5} \: cm$

So,

1st side = 3x = 3×5 = 15 cm

2nd side = 4x = 4×5 = 20 cm

3rd side = 5x =5×5 = 25cm

Hence,

perimeter of triangle = sume of all side

= 15+20+25 cm

= 60 cm

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Answer 2

Answer:

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