Question

The sides of a triangular field
are 51 m. 37m. and 20 m. Find the no. of rose beds that can be prepared in the
Field if each rose bed
occupies a Space of 6m2​

Answer 1

Step-by-step explanation:

Let sides of a triangular field be

a=20m,b=51m and c=37m

∴Semi−perimeter=

2

a+b+c

=

2

20+51+37

=

2

108

=54cm

∴Area of triangular field

=

s(s−a)(s−b)(s−c)

=

54(54−20)(54−51)(54−37)

=

54×34×3×17

=2×3×3×17

=18×17=306m

2

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.