Question

Any Best users?

$\sf \: \underline{ \boxed{Question:}}$

A rhombus-shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?​

Answer 1

$\large{\text{\underline{Let's begin:-}}}$

A rhombus has four properties.

➊Opposite sides are parallel to each other.

➋Opposite angles are equal.

➌The sum of adjacent angles is 180°.

➍Two diagonals are perpendicular bisectors of each other.

Here, we will use the fourth property.

$\large{\text{\underline{Solution:-}}}$

According to the property, the diagonals divide the rhombus into four right triangles.

Applying the Pythagorean theorem,

$\hookrightarrow \left(\dfrac{x}{2}\right)^{2}+(\dfrac{48}{2})^{2}=30^{2}$

Multiplying 4 on both sides,

$\hookrightarrow x^{2}+48^{2}=60^{2}$

$\hookrightarrow x^{2}=60^{2}-48^{2}$

Using a polynomial identity,

$\hookrightarrow x^{2}=(60+48)\cdot(60-48)$

$\hookrightarrow x^{2}=36^{2}$

We only count positive value as a length. Rejecting the negative solution,

$\hookrightarrow x=36\text{ (m)}$

The area of a rhombus is 4 times the area of right triangles made by diagonals.

$\hookrightarrow \text{(Area)}=4\times \dfrac{1}{2} \times 18\times 24$

$\hookrightarrow \text{(Area)}=864\text{ (m}^{2}\text{)}$

But as there were 18 cows, assuming all cows graze an equal amount,

$\hookrightarrow \text{(The area grazed by 1 cow)}=\dfrac{864}{18}$

$\hookrightarrow \text{(The area grazed by 1 cow)}=48\text{ (m}^{2}\text{)}$

$\large{\text{\underline{Answer:-}}}$

Each cow gets to graze $\text{48 m}^{2}$ of the green grass.

Answer 2

Answer:

Given :-

• A rhombus shaped field has green grass for 18 cows of cows to graze.If each side of the rhombus is 30m.and its longer diagonal is 48 m.

To find :-

• How much area of grass field will each cow be getting.

Solution :-

• Here we know the property such as ,Two diagonals are perpendicularly bisects each other.
• Here the diagonals divides the rhombus in four right angled triangles.

Now ,

• From phythagorous theorem we get that,

$( \frac{x}{2} ) {}^{2} + ( \frac{48}{2} ) {}^{2} = {30}^{2}$

• By solving this and multiplying 4 on both of the sides we get that,

• ${x}^{2} + {48}^{2} = {60}^{2}$
• Here we can use the polynomial identity for this equation to get perfect answer.
• ${x}^{2} = (60 + 48) \times (60 - 48) = {x}^{2} = {36}^{2}$
• By squaring on both the sides we get that,
• x=36m.

Now ,

• Here we should find the area
• We get that,

• $area = 4 \times \frac{1}{2} \times 18 \times 24 = 864 {m}^{2}$

Then,

• By dividing the area and number of crow to graze
• We get that,

• $= \frac{864}{18} = 48 {m}^{2}$

Therefore,

• The area of grass field will each cow be getting is 48m^2.

Hope it helps u mate .

Thank you .