Question

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

QUESTION:

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 6m²?

ANSWER:

Given:

• Sides of a triangular field = 51m,37m and 20 m
• Area taken by 1 rose bed = 6m²

To Find:

• Number of rose beds

Solution:

$\text{We know that, to find area of a triangle, }\\\\\:\longrightarrow\text{Heron's Formula:}=\sqrt{s(s-a)(s-b)(s-c)}\\\\\text{Where s is the semi-perimeter and a,b,c are the sides of the triangle.}\\\\:\implies s=\dfrac{Perimeter}{2}=\dfrac{a+b+c}{2}\\\\\text{Here, a=51m, b=37m, c=20m. So,}\\\\:\implies s=\dfrac{51+37+20}{2}=\dfrac{108}{2}\\\\:\implies s=54\\\\\text{Putting the values of s, a, b and c in the Heron's Formula. So,}\\\\:\implies Area=\sqrt{s(s-a)(s-b)(s-c)}\\\\:\implies Area=\sqrt{54(54-51)(54-37)(54-20)}\\\\:\implies Area=\sqrt{54(3)(17)(34)}\\\\:\implies Area=\sqrt{(2\times3\times3\times3)(3)(17)(2\times17)}\\\\:\implies Area=\sqrt{2\times3\times3\times3\times3\times17\times2\times17}$

$:\implies Area=\sqrt{2\times2\times3\times3\times3\times3\times17\times17}\\\\:\implies Area=\sqrt{2^2\times3^4\times17^2}\\\\:\implies Area=2\times3^2\times17=2\times9\times17\\\\:\implies Area=306m^2\\\\\text{We are given that, each rose bed takes 6m ^2 of area.}\\\\\text{So,}\\\\:\implies\text{Number of rose beds}=\dfrac{Total\:Area}{Area\:by\:each\:bed}=\dfrac{306}{6}\\\\\bf{:\implies\text{\bf{Number of rose beds}}=51}\\\\\text{So, there are 51 rose beds.}$

Formulae Used:

• Heron's Formula = √[s(s-a)(s-b)(s-c)]

Answer 2

Answer:

$51 \: rose \: beds$

Step-by-step explanation:

☘ Answer:-

☞ Area = √s(s-a)(s -b)(s-c)

=> A= √54 × 3 × 17 × 34 = 306 m².

Therefore,

No. of rose beds = 306/6 = 51.

__________________________

☘ Detailed solution:-

We know that,

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

Now, on substituting the known values of a, b, c from the above question, we get,

s = 51 + 37 + 20/2 = 108/2

= 54 cm.

Therefore,

Area of the triangular field as per the Heron's formula = √s(s-a)(s-b)(s-c)

= √54 (54-51) (54-37) (54-20)

= √54 × 3 × 17 × 34

= 306 m²

Now, the number of rose beds

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

right?...so, that's

= 306/6

and that gives,

☞ 51.

[The required answer].

Therefore,

The number of rose beds that can be prepared in the field if each rose bed occupies a space of 6 sq. m is 51.