Question

the sides of a triangula plot are in the ratio 3:5:7 & its Perimete is 3oom find the area.​

Answer 1

$\huge\mathbb{SOLUTION:-}$

• Given the sides of triangular plot in ratio
• 3:5:7
• we have to find the are

Now 1st fond the sides of plot

$\boxed{\sf{Perimeter\:of\:\triangle= sum\:of\:all\:sides}}$

• Let the side of plot be x

$\sf 3x+5x+7x=300\\ \\ \sf\leadsto 15x=300\\ \\ \sf\leadsto x=\cancel{\frac{300}{15}}= 20\\ \\ \sf\leadsto x=20$

• The value of x is 20
• Now the sides

• 3×20= 60m

• 5×20=100m

• 7×20=140m

Now we have to find the area of triangle

By heron's formula

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

$\sf {\blue{s=\dfrac{a+b+c}{2}}}\\ \\ \sf\implies s=\dfrac{60+100+140}{2}\\ \\ \sf\implies s=\cancel{\dfrac{300}{2}}= 150\\ \\ \sf\implies s= 150m$

Now the area of ∆

$\sf\implies Area=\sqrt{150(150-60)(150-100)(150-140)}\\ \\ \sf\implies Area \sqrt{150\times 90\times 50\times 10}\\ \\ \sf\implies Area=\sqrt{3\times 50\times 3\times 10\times 3\times 50\times 10}\\ \\ \sf\implies Area=3\times 50\times 10\sqrt{3}\\ \\ \sf\implies Area= 1500\sqrt{3}m{}^{2}$

$\boxed{\sf{\red{Area\:of\:\triangle=1500\sqrt{3}m{}^{2}}}}$

Answer 2

Question :--- The sides of a triangula plot are in the ratio 3:5:7 & its Perimeter is 300m.. find the area. ?

Formula and concept :-----

Triangle :--- is a plane figure with three straight sides and three angles.

→ Area of ∆ = 1/2 * Base * Height = 1/2* ab* sinC = 1/2 * bc *sinA = 1/2 * ca* sinB = √( s(s-a)(s-b)(s-c) ) [ where s = (a+b+c)/2 ]

→ There are three special names given to triangles that tell how many sides (or angles) are equal:---

1) Equilateral Triangle :-- Have Three equal sides and Three equal angles, always 60°..

2) Isosceles Triangle :-- Have Two equal sides and Two equal angles..

3) Scalene Triangle :-- No equal sides and No equal angles...

→ Triangles can also have names that tell you what type of angle is inside: ---

1) Acute Triangle = All angles are less than 90°..

2) Right Triangle = Has a right angle (90°)..

3) Obtuse Triangle = Has an angle more than 90°..

→ The three interior angles always add to 180°...

______________________________

Solution :----

since sides of ∆ are in ratio 3:5:7,

→ let these sides are 3x , 5x and 7x respectively.

Now, Perimeter of ∆ is given as = 300m.

So,

→ 3x + 5x + 7x = 300

→ 15x = 300

Dividing both sides by 15 we get,

→ x = 20 .

Hence, sides are

→ 3x = 3*20 = 60m

→ 5x = 5*20 = 100m

→ 7x = 7*20 = 140m

_____________________________

So,

→ Semi-perimeter of ∆ = (60+100+140)/2 = 150m.

Required Area of ∆ = √s(s-a)*(s-b)*(s-c)

→ Area = √150*(150-60)*(150-100)*(150-140)

→ Area = √150*90*50*10

→ Area = √3*50*3*30*50*10

→ Area = √(3*3)*(50*50)*(10*10)*3

→ Area = 3*50*10√3

→ Area = 1500√3m²

Hence , Area of Required ∆ is 1500√3m².