Question

Q. 5. The sides of a triangular field are 51 m, 27 m 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 m2​

Answer 1

Given :-

• The sides of a triangular field are 51 m, 27 m and 20 m.

• Each rose bed occupies a space of 6 m².

To Find :-

• The number of rose beds.

Solution :-

We know that,

The semi perimeter ( s ) of any traingle =

S = $\dfrac{(a + b + c) }{2}$

According to the question,

a = 51 m

b = 27 m

c = 20 m

s = $\dfrac{(51 + 37 + 20) }{2}$

➝ $\cancel{\dfrac{(108) }{2}}$

➝ 54 cm.

Using, Heron's formula

The Area of the triangular field

➝ √s(s-a)(s-b)(s-c)

➝ √54 (54-51) (54-37) (54-20)

➝ √54 × 3 × 17 × 34

➝ √ 93636

➝ 306 m²

Given, the number of rose beds occupies a space of 6 m².

Total area of the triangular field is 306 m².

Hence, The number of rose beds =

$\dfrac{Total \: area}{Area \: occupied \: by \: bed}$

➝ $\cancel{\dfrac{306}{6}}$

➝ 51 beds.

Thier are 51 rose beds on the triangular field .

_____________________________________

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.