Question

the sides of a triangular park is in the ratio 3:5:7. it's semi perimeter is 150 m find its area​

Answer 1

Answer :

›»› The area of triangular park is 1500√3 m².

Given :

• The sides of a triangular park is in the ratio 3:5:7.

To Find :

• The area of triangular park.

Solution :

Let us assume that, the sides of a triangular park is 3x, 5x, and 7x respectively.

As it is given that the semi perimeter is 150 m.

And their sides are :

• a = 3x.
• b = 5x.
• c = 7x

As we know that

→ s = (a + b + c)/2

→ 150 = (3x + 5x + 7x)/2

→ 150 = (8x + 7x)/2

→ 150 = 15x/2

→ 150 * 2 = 15x

→ 300 = 15x

→ x = 300/15

→ x = 20

Therefore,

→ a = 3x

→ a = 3 * 20

→ a = 60

→ b = 5x

→ b = 5 * 20

→ b = 100

→ c = 7x

→ c = 7 * 20

→ c = 140

Their sides are 60, 100, and 140.

Now,

As we know that

→ Area = √s(s - a)(s - b)(s - c)

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

→ Area = √150 * 90 * 50 * 10

→ Area = √(150 * 9 * 5) * (10)⁴

→ Area = √15 * (3 * 3) * 5 * 3 * (10)⁴

→ Area = √15 * (3 * 5) * 3 * (10)⁴

→ Area = √15 * 15 * 3 * (10)⁴

→ Area = √(15)² * 3 * (10)⁴

→ Area = √(15)² * √3 * √(10)⁴

→ Area = (15) * √3 * (10⁴)^½

→ Area = (15) * √3 * (10²)

→ Area = 15 * √3 * 1000

→ Area = 1500√3

Hence, the area of triangular park is 1500√3 m².

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• Ratio of sides of triangular park is 3:5:7

$\:\:$

• Semi perimeter is 150 m

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• Area of triangular park

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

$\underline{\bold{\texttt{Area of triangle : }}}$

$\:\:$

$\bf \dag \ \sqrt {s(s - a)(s - b)(s - c) }$

$\:\:$

• s = Semi perimeter

• a = 1st side

• b = 2nd side

• c = 3rd side

$\:\:$

Let the sides be 3x , 5x , 7x respectively

$\:\:$

$\sf \longmapsto s = 150 \ \ \ \ [ Given ]$

$\:\:$

Also,

$\:\:$

$\sf \longmapsto s = \dfrac { (a + b + c) } { 2 }$

$\:\:$

$\sf \longmapsto 150 = \dfrac { 3x + 5x + 7x } { 2 }$

$\:\:$

$\sf \longmapsto 300 = 3x + 5x + 7x$

$\:\:$

$\sf \longmapsto 300 = 15x$

$\:\:$

$\bf \dashrightarrow x = 20$

$\:\:$

• a = 3 × 20 = 60m

• b = 5 × 20 = 100m

• c = 7 × 20 = 140m

$\:\:$

$\underline{\bold{\texttt{For area -}}}$

$\:\:$

$\sf \longmapsto \sqrt {150(150 - 60)(150 - 100)(150 - 140) }$

$\:\:$

$\sf \longmapsto \sqrt {150(90)(50)(10) }$

$\:\:$

$\sf \longmapsto \sqrt {6750000 }$

$\:\:$

$\bf \dashrightarrow 1500 \sqrt 3$

$\:\:$

• Hence area will be 1500√3

Or

• 2598 sq. m [ Approx ]