Question

The sides of a triangular field are 51m, 37m, and 20m. Find the number of rose

beds that can be prepared in the field if each rose bed occupies a space of

6sq.m.​

Answer 1

Step-by-step explanation:

s or semi perimeter = a+b+c /2

so, 51+37+20/2 = 108/2 = 54cm

using heron formula

$\sqrt{?} s(s - a)(s - b)(s - c)$

5

Answer 2

$\huge\fbox\red{A}\huge\fbox\pink{N}\fbox\green{S}\huge\fbox\blue{W}\fbox\orange{E}\huge\fbox\red{R}$

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

⠀

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

S E M I – P E R I M E T E R :

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

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

$\rule{250px}{.3ex}$

F I N D I N G⠀A R E A :

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

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

$\underline{\bf{\dag} \:\mathfrak{Substituting\;given\;values\: :}}$

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

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⠀

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

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