Question

Sides of a right triangular field are 25m, 24m and 7m. At the three corners of the field, a
cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the
field. Find the area of the field that cannot be grazed by these animals.​

Answer 1

Answer:

Step-by-step explanation:

Area of triangle = area of rectangle/2

Theta/360 * 22/7* 3.5 *3.5

Answer 2

Area of Field that can't graze is 64.75 m²

Explanation :

Given :

Sides of Right Triangular Field :

• Hypotenuse = 25 m
• Perpendicular = 24 m
• Base = 7 m
• A Cow, A Buffalo, and A Horse are tied separately with ropes of 3.5 m at three corners.

To Find :

The area of the field that cannot be grazed by these animals.​

Solution :

Step 1 :

• Find the Total Area :

Let the sides of Triangle be ABC,

So,

$\implies \sf Area_{\tiny ABC} =\dfrac{1}{2} \times Base \times Height \\ \\ \\\implies \sf Area_{\tiny ABC} =\dfrac{1}{2} \times7 \times 24 \\ \\ \\ \implies \sf Area_{\tiny ABC} =\dfrac{1}{ \cancel2} \times\cancel{168} \\ \\ \\ \implies \sft Area_{\tiny ABC} = 84 \: {m}^{2}}$

∴ Total Area of Grass Field is 84 m²

$\rule{300}{1.5}$

Step 2 :

• Area that Animals can Graze are :

$\implies \sf Area = \dfrac{\angle A}{360\degree}\pi {r}^{2} + \dfrac{\angle B}{360\degree}\pi {r}^{2} + \dfrac{\angle C}{360\degree}\pi {r}^{2} \\ \\ \\\implies \sf Area = \pi {r}^{2} \bigg(\dfrac{\angle A}{360\degree}+ \dfrac{\angle B}{360\degree} + \dfrac{\angle C}{360\degree} \bigg)\\ \\ \\ \implies \sf Area = \pi {r}^{2} \bigg(\dfrac{\angle A +\angle B +\angle C}{360\degree}\bigg) \\ \\ \\ \implies \sf Area = \pi {r}^{2} \bigg( \cancel\dfrac{180 \degree}{360\degree}\bigg)$

$\implies \sf Area = \dfrac{22}{7} \times 3.5 \times 3.5 \times \dfrac{1}{2} \\ \\ \\ \implies \sf Area =19.25 \: {m}^{2}$

∴ Total Area that can Graze is 19.25 m²

$\rule{300}{1.5}$

Step 3 :

• Area that can't be Graze is :

$\bigstar\;\boxed{\textbf{Area Can't Graze = Total Area of Field - Area Can Graze}}$

⇒ Area Can't Graze = (84 - 19.25) m²

⇒ Area Can't Graze = 64.75 m²

Hence,

Area of Field that can't graze is 64.75 m²

$\rule{300}{1.5}$

• Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\put(7.7,2.9){\large{A}}\put(7.7,1){\large{B}}\put(10.6,1){\large{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\put(10.5,1){\line(-4,3){2.5}}\put(7.3,2){\mathsf{\large{24 m}}}\put(9,0.7){\matsf{\large{7 m}}}\put(9.4,1.9){\mathsf{\large{25 m}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\end{picture}$