The sides of triangular field are 51m ,37m and 20m.Find the number of flower beds that can be prepared ,if each bed is to occupy 9m sq.of apace
Answers
Answer:
Step-by-step explanation:
s= a+b+c/2
51 +37+20/2
=54
area = √s(s-a)(s-b)(s-c)
= √54 (54-51)(54-37)(54-20)
=√54(3)(17)(34) {simplest form}
= √(3*2*3*3)*(3)*(17)*(17*2)
= 3*2*3*17
= 306m²
area needed for flower beds
= 306/9
= 34
∴ 34 flower beds are required to occupy the space
☘ 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.
__________________________