Question

2. A rhombus-shaped field has green grass for 36 cows to graze. If each side of the field is 30 m
and the longer diagonal is 48 m, then how much area of grass each cow will get, IF 216m^2of
area is not to be grazed? *
(1 Point)
O 6m^2
12 m^2
18 m^2
20 m^2

Answer 1

Given :-

Number of cows = 36 cows

Length of the side of field = 30 m

Longer diagonal of the field = 48 m

Area not to be gazed = 216 m²

To Find :-

Area the each cow gets.

Analysis :-

A diagonal divides the rhombus into two congruent triangles which are having equal areas.

Find the semi perimeter of the triangle by adding all the sides divided by two.

Next, using Heron's formula substitute the values got and find the area of the triangle accordingly.

Multiply the area we got by two. (Since we divided the rhombus into two parts)

Substract the area not to be gazed from the area we got.

Divide the new area by the number of cows in order to find the area each cow gets.

Solution :-

We know that,

• s = Semi perimeter
• a = Area

A diagonal divides the rhombus into two congruent triangles which are having equal areas.

By the formula,

$\underline{\boxed{\sf Semi \ perimeter=\dfrac{a+b+c}{2} }}$

Given that,

a = 48, b = 30, c = 30

Substituting their values,

s = 48+30+30/2

s = 108/2

s = 54 m

Using Heron’s formula,

$\underline{\boxed{\sf Area \ of \ triangle=\sqrt{s(s-a)(s-b)(s-c)} }}$

Given that,

Semi perimeter = 54 m

a = 48, b = 30, c = 30

Substituting their values,

$\sf =\sqrt{54(54-48)(54-30)(54-30)}$

$\sf =\sqrt{54 \times 6 \times 24 \times 24}$

$\sf =\sqrt{186624 }$

$\sf =432 \ m^2$

∴ Area of field = 2 × area of the triangle

= (2 × 432) = 864 m²

Given that,

216 m² of area is not to be gazed.

Then,

Area of the field - 216

= 864 - 216

= 648 m²

According to the question,

Number of cows = 36 cows

Area with us = 648 m²

Finding the area of each cow,

a = 648/36

a = 18 m²

Therefore, 18 m² of area will be required for each cow.