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, each cow will be getting ______m2 area of grass field to graze. a) 64 b) 48 c) 864 d) 432 *​

Answer 1

Answer

Option b) 48 m²

$\rule{200}2$

Explanation

A rhombus shaped field has green grass for 18 cows to graze.

Total number of cows = 18

Also given that, each side of the rhombus is 30 m and its longer diagonal is 48 m.

Let us assume that ABCD is a rhombus having sides 30 m and of diagonal 48 m.

(as shown in fig.)

In ∆ABD

Semi-perimeter of triangle = (a + b + c)/3

a = 30, b = 30 and c = 48

→ (30 + 30 + 48)/3

→ 108/3

→ 54 m

Area of triangle = √[s(s - a)(s - b)(s - c)]

→ √[54(54 - 30)(54 - 30)(54 - 48)]

→ √[54(24)(24)(6)

→ √[(6*9)(8*3)(8*3)(6)]

→ √[(6*6)(9)(24*24)]

→ 6 × 3 × 24

→ 432 m²

Similarly, Area of ∆BCD = 432 m²

Area of rhoumbus ABCD = Ar.(∆ABD + ∆BCD)

→ (432 + 432) m²

→ 864 m²

Now,

Area of each cow = (Area of rhombus ABCD)/(Total number of cows)

→ 864/18

→ 48 m²

Answer 2

||✪✪ 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, each cow will be getting ______m2 area of grass field to graze. a) 64 b) 48 c) 864 d) 432 *

|| ★★ FORMULA USED ★★ ||

• Diagonals of a Rhombus Bisect each other at 90° in equal parts .
• Pythagoras Theoram .
• Area of Rhombus = 1/2 * Diagonal1 * Diagonal2

|| ✰✰ ANSWER ✰✰ ||

❁❁ Refer To Image First .. ❁❁

From image we can see That ∆DOC is a right angle ∆ right angle at O, and DC is hypotenuse .

Let DO is x m.

Than, using Pythagoras theoram we Get :-

→ X = √(30)² - (24)²

→ x = √(900 - 576)

→ x = √(324)

→ x = 18m. = DO.

So, Diagonal DB = 2*18 = 36m.

So,

→ Area of Rhombus = (1/2) * 36 * 48 = (18 * 48)m²

____________

Now, In Rhombus Shaped Field Their were grass for 18 cows to graze .

So,

→ Each cow graze Area of Field = (Total Area)/18 = (18*48)/18 = 48m². (Option B).

Hence, each cow will be getting 48m² area of grass field to graze.