Question

the sides of a triangular park are in the ratio 3:5:7 and its perimeter 600m. Find the area of the given park​

Answer 1

Question:

The sides of a triangular park are in the ratio 3:5:7 and its perimeter 600m. Find the area of the given park.

To find:

• Area of triangular park

Given:

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

• perimeter = 600m

Let:

• Side 1 = 3x
• Side 2 = 5x
• Side 3 = 7 x

Explanation:

So first we have to suppose the side which are in ratio of 3:5:7 as 3x , 5x,7x. And then by using formula of Perimeter i.e.p=s1+s2+s3 , we will find value of x. Then by using this value of x we can find length of each side . When we will get length of each side , then by using herons formula we can find area.

Answer:

We know:

$\sf Perimeter \: of \: triangle =side \: 1+ side \: 2 +side \: 3$

By using this formula we can find value of x

And after getting value of x we can find each side of triangle

$\therefore \sf \:600 = 3x + 5x+ 7x$

$: \implies \sf \:600 = 15x$

$: \implies \sf x = \dfrac{600}{15}$

$: \implies\sf x = \dfrac{ { \cancel{600}}^{ \ \: \: 40} }{ { \cancel{15}}^{ \: \: 1} }$

$: \implies \star \boxed{ \sf{x = 40}} \star$

$\text{Now Let's find length of each side}$

$\sf{ \green{side \: 1 = 3x}}$

$\sf{ \implies \green{side \: 1 = 3 \times 40}}$

$\sf{ \implies \green{side \: 1 = 120 \: m}}$

$\sf{ \pink{side \: 2= 5x}}$

$\sf{ \implies \pink{side \: 2 = 5\times 40}}$

$\sf{ \implies \pink{side \: 2 =200 \: m}}$

$\sf{ \blue{side \: 3 = 7x}}$

$\implies \sf{ \blue{side \: 3 = 7 \times 40}}$

$\implies \sf{ \blue{side \: 3 = 280 \: m}}$

As in question it's asked to find Area.

Let's find it by using heroes formula:

To find area first we have to find semi perimeter (s)

$\sf \: s = \dfrac{a + b + c}{100}$

$: \implies \sf \: s = \dfrac{120+ 200+ 280}{2}$

$: \implies\sf \: s = \dfrac{600}{2}$

$: \implies\sf \: s = \dfrac{ {\cancel{600}}^{ \: 300} }{ {\cancel{2}}^{ \: 1} }$

$: \implies\sf \: \star{} \boxed{ \sf s = 300} \star$

Now Let's find Area of triangle:

$\sf{}Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

$: \implies \sf{}Area \: of \: triangle = \sqrt{300(300 - 120 )(300 - 200)(300- 280)}$

$: \implies \sf{}Area \: of \: triangle = \sqrt{300 \times 180 \times 100 \times 20}$

$:\implies \sf{}Area \: of \: triangle = \sqrt{108000000}$

$:\implies \star\boxed{\sf{}Area \: of \: triangle=10,392.30cm²}\star$

$\red{\text{And all we are done! ✔}}$

;)