Question

(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 1

Given:

• The sides of a triangular field are 51m,37m and 20 m.

To Find:

• Number of rose beds that can be prepared in the field if each rose bed occupies a space of 6m

Solution:

First of all we need to find area of triangular field using heron's formula.

Semi - Perimeter :

s = 51 + 37 + 20/2

= 108/2

= 54 m.

Therefore,

Using Heron's formula :

= √s(s-a)(s-b)(s-c)

= √54 (54-51) (54-37) (54-20)

= √54 × 3 × 17 × 34

= 306 m²

Now,

Number of rose beds that can be prepared in field if each rose bed occupies a space of 6m :

= Total area of the triangular field/ Area occupied by each rose bed.

= 306/6

= 51

Hence, 51 rose beds can be prepared in the field if each rose bed occupies a space of 6m

Answer 2

❍ 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 :

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

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

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F I N D I N G⠀A R E A :

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

⠀

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

⠀

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

⠀

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

⠀

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

⠀

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