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(1) The sides of a triangular field are 51m,37m and 20 m. Find the number of rose beds that can be prepared in the field if each rose bed occupies a space of 6 m?​

Answer»

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❍ Sides of the Triangular filed are 20 m, 37 m and 51 m respectively.

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To Calculate AREA of the triangle we'll use Heron's formula. Heron's formula is used to calculate the area of triangle.

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S E M I – P E R I M E T E R :

\bf{\dag}\;\;\boxed{\sf{Semi - Perimeter = \bigg(\dfrac{Sum\;of\;all\; sides}{2}\bigg)}}

:\implies\sf S = \dfrac{a + b + c}{2}\\\\\\:\implies\sf S = \dfrac{51 + 37 + 20}{2} \\\\\\:\implies\sf S =\cancel \dfrac{ 108}{2}\\\\\\:\implies\underline{\boxed{\frak{S = 54\;m}}}

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F I N D I N G⠀A R E A :

\bf{\star}\;\boxed{\sf{Area_{\triangle} = \Big(\sqrt{s(s - a)(s - b)(s - c)}\;\Big)}}

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\frak{we\;have}\begin{cases}\sf{ \: \: a = 20 \;m}&\\\sf{ \: \: b = 51\:m}&\\\sf{ \: \: c = 37\;m}&\\\sf{ \: \: s = 54\;m}\end{cases}

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\underline{\bf{\dag} \:\mathfrak{Substituting\;<klux>GIVEN</klux>\;values\: :}}⠀⠀⠀⠀

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:\implies\sf Area_{\triangle} = \sqrt{54(54 -20)(54 - 51)(54 - 37)}\\\\\\:\implies\sf Area_{\triangle} = \sqrt{54 \times 34 \times 3 \times 17} \\\\\\:\implies\sf Area_{\triangle} = \sqrt{2\times 3\times 3 \times 3 \times 2 \times 17 \times 3 \times 17}\\\\\\:\implies\sf Area_{\triangle} = 2 \times 3 \times 3 \times 17\\\\\\:\implies\underline{\boxed{\frak{\pink{Area_{\triangle} = 306\;m^2}}}}\;\bigstar

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N O.⠀O F⠀R O S E :

  • It is given that, each rose bed occupies space of 6 m. Therefore,

➠ AR. or field/Ar. of rose

➠ 306/6

➠ 51

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\therefore{\underline{\textsf{Hence, \;number\;of\;roses\;that\;can\;be\; prepared\;are\;\textbf{51}.}}}⠀⠀⠀⠀


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