What are lengths of sides of a triangle whose perimeter is 540 m and sides are in the ratio 25 17 12?

The sides of a triangle are in the ratio 25 : 17 : 12

Let the sides of a triangle are a = 25x, b = 17 x and c = 12x say.Perimeter = 25 = a + b + c = 540 cm⇒ 25x + 17x + 12x = 540 cm

⇒ 54x = 540cm

⇒ x = `540/54`⇒ x = 10 𝑐𝑚

∴ The sides of a triangle are a = 250 cm, b = 170 cm and c = 120 cm

Now, Semi perimeter s =`(a+b+c)/2`

`=(540)/2=270cm`

∴The aera of the triangle =`sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(270(270-250)(270-170)(270-120))`

`=sqrt(27(20)(100)(150))`

`sqrt((9000)(9000))`

`9000 cm^2`\

The aera of triangle = `900cm^2`

Page 2

Given thatThe perimeter of a triangle = 300 mThe sides of a triangle in the ratio 3 : 5 : 7Let 3x, 5x, 7x be the sides of the trianglePerimeter ⇒ 2s = a + b + c⇒ 3x + 5x + 17x = 300⇒ 15x = 300⇒ x = 20mThe triangle sides are a = 3x= 3 (20)m = 60 mb = 5x = 5(20) m = 100m

c = 7x = 140 m

semi perimeter s = `(a+b+c+)/2`

`=(300)/2m`

`=150m`

∴The area of the triangle `=sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(150(150-60)(150-100)(150-140))`

`=sqrt(150xx10xx90xx50)`

`=sqrt(1500xx1500) 3 cm^2`

`∴Δ` le Area = 1500 `sqrt3 cm^2`

Question 6 Areas Of Triangles And Quadrilaterals Exercise 14

Answer:

Consider a, b, c as the sides of a triangle in the ratio 25: 17: 12

It can be written as

a: b: c = 25: 17: 12

So we get

a = 25, b = 17 and c = 12

It is given that

Perimeter = 540 m

So we get

25x + 17x + 12x = 540

On further calculation

54x = 540

By division

x = 10

By substituting the value of x

a = 25x = 25(10) = 250m

b = 17x = 17(10) = 170m

c = 12x = 12(10) = 120m

We know that

Area = $9000\mathrm{m}^2$

It is given that the cost of ploughing the field is ₹ 5 per $\mathrm{m}^2$

So the cost of ploughing $9000\mathrm{m}^2$ = 5 × 9000

By multiplication

The cost of plowing $9000\mathrm{m}^2$ = ₹ 45000

Therefore, the area of the field is $9000\mathrm{m}^2$ and the cost of ploughing the field is ₹ 45000

Video transcript

"hello students i am data your mass leader tutor and the today's question is the perimeter of a triangular field is 540 meter and its side are in the ratio 25 is to 17 is to 12 find the area of the field and also find the cost of plugging the fill at rupees 5 per meter square so it's flowing it's not flowing it's showing find the cost of showing the fill at rupees 5 per meter square first of all in this question the perimeter is given to us 540 and the sides are given to us so we add parameters first of all we let the sides are the sides of triangle are 25x 17x and 12x now the perimeter is given to us so we apply the formula perimeter is equal to sum of all sides so we add all these sides 25x plus 17x plus 12x that is equal to 540 meter is equal to when we add them 25 plus 10 35 plus 10 45 plus 9 we got 54 x then we divide 540 divided by 54 then we got the value of x that is equal to 10 meter now we got the value of x that is 10 meter now we put the value of x in all the three sides then we got 25 into 10 that is 250 meter and 17 in x that is equal to 17 into 10 is equal to 170 meter and 12 x that is 12 into 10 that is equal to 120 meter now we find the area area is equal to first of all for that we have to find the value of s as is the semi perimeter a plus b plus c by 2 when we add all first of all we have to the sum of all sides it means perimeter is given to us 540 divided by 2 so we got two 2s of 4 14 now we find the area of triangle when all the three sides are given to us the formula is s as minus a as minus b as minus c now we substitute the values of s and abc the value of s is 270 270 minus 250 270 minus 170 and 250 minus sorry it's 270 minus 170 and 270 minus 120 now we solve this then we got this square root 270 into 20 into 100 into zero seven minus two five two minus one one one fifty now we break them into their prime factor nine threes are twenty seven or we can write this three threes are nine threes are 27 tenza and this is a ninth 27 into 10 2 into 10 we can write 100 as 10 into 10 and we can write 150 as three fives up 15 into 10 now we make a pair one and there are two pairs of three so three into three and one two and one there are how many pairs of ten so two pairs of three and 2 we can write 10 as 2 into 5 we can write this 10 as 2 into 5 so we have one pair of 2 and one pair of five and two pair of ten now we multiply them ten into ten hundred into five five hundred into two thousand thousand into three thousand into nine that is nine thousand meter square now the area is given now we find the area that is nine thousand meter square now we have to find the cost of showing the field at rupees 5 per meter square now we have to find the cost also so cost of cost of showing the field is five meter per square meter so for nine thousand we multiply them from five then we got five times of 45 000 rupees so this is the cost of showing stuff filled i hope you like this video so please subscribe to for more updates and do comment your questions thank you "

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The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the field. Also, find the cost of ploughing the field at Rs 5 per m2,

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