Question

The area of the triangle is 150cm².and its sides are in the ratio 3:4:5. what is it's perimeter?

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Answer 1

Step-by-step explanation:

GIVEN

AREA of the triangle is 150cm²

Ratio of sides → 3:4:5.

TO FIND

Perimeter

SOLUTION

Let the sides be X

a = 3x

b = 4x

c = 5x

Using Heron's Formula,

s = (3+4+5)x/2 = 12x/2 = 6x

\begin{gathered} \begin{gathered} \sqrt{s(s - a)(s - b)(s - c)} \\ \sqrt{6x(6x - 3x)(6x - 4x)(6x - 5x)} \\ \sqrt{6x \times 3x \times 2x \times x} \\ \sqrt{36 {x}^{4} } \\ 6 {x}^{2} \\ Area = 150 \: {cm}^{2} \\ So, \\ 6 {x}^{2} = 150 \\ {x}^{2} = \frac{150}{6} \\ {x}^{2} = 25 \\ x = \sqrt{25} = 5 \: cm\end{gathered} \end{gathered}

s(s−a)(s−b)(s−c)

6x(6x−3x)(6x−4x)(6x−5x)

6x×3x×2x×x

36x

4

6x

2

Area=150cm

2

So,

6x

2

=150

x

2

=

6

150

x

2

=25

x=

25

=5cm

Therefore,

a = 5×3 = 15 cm

b = 5×4 = 20 cm

c = 5×5 = 25 cm

NOW,

Perimeter

= 15+20+25

= 60 cm

Answer 2

The perimeter is 60 cm

hope it helps you ✌