Question

Three horses are tethraded at three corners of triangular field with a rope of length 7 m. How much

area inside the field, they can grage​

Answer 1

SOLUTION

the area they can grage is 21 cm

THE AREA IF TRIANGLE IS EQUAL TO THE AREA THEY CAN GRAGE

HOPE IT HELPS AND MARK ME AS A BRAINLIST

Answer 2

Answer:

Hint:We know that the sum of all the angles of the triangle is 180∘ and the length of the rope of each horse is 7 meters. Hence, they will form the arc of equal radius. And, the sum of all the angles formed of the respective arc at each corner by the horses is also equal to 180∘ . So, the total area grazed by all the three horses will be equivalent to the area of the semicircle which is of radius 7 m. Area of each arc will be given by area=θ360∘×π×r2 and to find area of ungrazed part we will subtract the area of ungrazed part from area of the triangle by using formula area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−−√

where s is a semi-perimeter of the triangle s=a+b+c2 .

Complete step-by-step answer:

We know from the question that the length of the rope of each horse is equal to 7 m. Hence, the maximum area of the field which can be grazed by each horse will be equal to the sum of the area of the sector which each horse will make at each corner of the field. Since, the angle of each sector will be equal to the angle made by two respective sides of the triangle.

Let us assume that α , β and γ are the angles made by the sides of the triangle.

So, α+β+γ=180∘

So, the angles made by each of the respective arcs are also α , β and γ .

Here, radius of each arc = 7 m

So, the total area of the field which is grazed = Area of the arc made by the horse at A + Area of the arc made by the horse at B + area of the arc made by the horse at C.

=α360∘×π×(7)2+β360∘×π×(7)2+γ360∘×π×(7)2m2

=(α+β+γ)360∘×π×7m2

Since, α+β+γ=180∘

=180∘360∘×π×(7)2m2

=π×492m2

=76.969m2

Hence, the total area grazed by the horse is 76.969m2 . Now, we find the area of the triangle:

So, area of the triangle ΔABC is given by:

area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−−√ where, s=a+b+c2

So, s=20+34+422 = 962=48m

So, area of triangle is 48(48−20)(48−34)(48−42)−−−−−−−−−−−−−−−−−−−−−−−−−√m2

=48×28×14×6−−−−−−−−−−−−−√m2

=336m2

Hence, the area of the ungrazed part = Area of triangle – Area of the grazed part =336m2−76.969m2

=259.031m2

Hence, area of the field which can be grazed is equal to 76.969m2 and the area of the ungrazed part is equal to 259.031m2 .