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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2 thoughts on “The area of the triangle is 150cm².and its sides are in the ratio 3:4:5. what is it’s perimeter?<br /><br />✘ɴᴏ sᴘᴀᴍ<br />✘ɴᴏ ᴄᴏᴘɪ”

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

   Reply

2. The perimeter is 60 cm

   hope it helps you ✌

   Reply