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Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

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Ratio of the sides of the triangle = 12 : 17 : 25 Let the common ratio be x then sides are 12x, 17x and 25x Perimeter of the triangle = 540cm 12x + 17x + 25x = 540 cm ⇒ 54x = 540cm ⇒ x = 10 Sides of triangle are, 12x = 12 × 10 = 120cm 17x = 17 × 10 = 170cm 25x = 25 × 10 =...
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Ratio of the sides of the triangle = 12 : 17 : 25
Let the common ratio be x then sides are 12x, 17x and 25x
Perimeter of the triangle = 540cm
12x + 17x + 25x = 540 cm
⇒ 54x = 540cm
⇒ x = 10
Sides of triangle are,
12x = 12 × 10 = 120cm
17x = 17 × 10 = 170cm
25x = 25 × 10 = 250cm
Semi perimeter of triangle(s) = 540/2 = 270cm
Using Heron's formula,

 
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Let the sides of the triangle be 12x, 17x & 25x. ∴ 12x + 17x + 25x = 540cm ⇒ 54x = 540 ⇒ x = 540/54 = 10. ∴ the sides are 12 × 10 = 120cm, 17 × 10 = 170cm & 25 × 10 = 250cm. ∴ the area of the triangle = √270 ( 270 - 120 )( 270 - 170 )( 270...
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Let the sides of the triangle be 12x, 17x & 25x.

∴ 12x + 17x + 25x = 540cm ⇒ 54x = 540

⇒ x = 540/54 = 10.

∴ the sides are 12 × 10 = 120cm, 17 × 10

= 170cm & 25 × 10 = 250cm.

∴ the area of the triangle

= √270 ( 270 - 120 )( 270 - 170 )( 270 - 250)

√ 270 X 150 X 100 X 20 = 100√ 27 X 15 X 10 X 2 = 100√ 3 X 3 X 3 X 3 X 5 X 5 X 2 X 2 = 100 X 3 X 3 X 5 X 2 = 9000cm².

 

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Let the sides of the triangle be 12x, 17x & 25x. ∴ 12x + 17x + 25x = 540cm ⇒ 54x = 540 ⇒ x = 540/54 = 10. ∴ the sides are 12 × 10 = 120cm, 17 × 10 = 170cm & 25 × 10 = 250cm. ∴ the area of the triangle = √270 ( 270 - 120 )( 270 - 170 )( 270...
read more

Let the sides of the triangle be 12x, 17x & 25x.

∴ 12x + 17x + 25x = 540cm ⇒ 54x = 540

⇒ x = 540/54 = 10.

∴ the sides are 12 × 10 = 120cm, 17 × 10

= 170cm & 25 × 10 = 250cm.

∴ the area of the triangle

= √270 ( 270 - 120 )( 270 - 170 )( 270 - 250)

√ 270 X 150 X 100 X 20 = 100√ 27 X 15 X 10 X 2 = 100√ 3 X 3 X 3 X 3 X 5 X 5 X 2 X 2 = 100 X 3 X 3 X 5 X 2 = 9000cm².

 

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Professional teacher with 5 years of experiance.

Lets the sides be 12x ,17x and 25x respectively. Its perimeter = 12x + 17x + 25x which is 540cm Therefore , according to the question 12x +17x+25x = 540 29x +25x = 540 54x = 540 X = 540/54 X = 10. Therefore the sides are 12×10 =120 17×10= 170 25×10 = 250 Therefore area of the triangle...
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Lets the sides be 12x ,17x and 25x respectively.

Its perimeter = 12x + 17x + 25x which is 540cm 

Therefore , according to the question

12x +17x+25x = 540

29x +25x = 540

54x = 540

X = 540/54

X = 10. 

Therefore the sides are 12×10 =120

17×10= 170

25×10 = 250

Therefore area of the triangle = √S(s-a)(s-b)(s-c)

=√270(270-120)(270-170)(270-250)

=√270×150×100×20

=√3×3×3×10×3×5×10×2×2×5×5×2×10

=9000cm²

Area of the triangle is 9000cm²

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Comments

Professional teacher with 5 years of experiance.

Lets the sides be 12x ,17x and 25x respectively. Its perimeter = 12x + 17x + 25x which is 540cm Therefore , according to the question 12x +17x+25x = 540 29x +25x = 540 54x = 540 X = 540/54 X = 10. Therefore the sides are 12×10 =120 17×10= 170 25×10 = 250 Therefore area of the triangle...
read more

Lets the sides be 12x ,17x and 25x respectively.

Its perimeter = 12x + 17x + 25x which is 540cm 

Therefore , according to the question

12x +17x+25x = 540

29x +25x = 540

54x = 540

X = 540/54

X = 10. 

Therefore the sides are 12×10 =120

17×10= 170

25×10 = 250

Therefore area of the triangle = √S(s-a)(s-b)(s-c)

=√270(270-120)(270-170)(270-250)

=√270×150×100×20

=√3×3×3×2×5×3×5×2×5×2×2×5×5×2×2×5

=9000cm²

Area of the triangle is 9000cm²

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9000
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Mathematics & Science Tutor Having 14 yrs of Experience.

12x +17x+25x =540 X = 12.27 cm.
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Certified Cardiologist Technician

Let the common ratio between the sides of the given triangle be x. Therefore, the side of the triangle will be 12x, 17x, and 25x. Perimeter of this triangle = 540 cm 12x + 17x + 25x = 540 cm 54x = 540 cm x = 10 cm Sides of the triangle will be 120 cm, 170 cm, and 250 cm. Therefore, the area of this...
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Let the common ratio between the sides of the given triangle be x.

Therefore, the side of the triangle will be 12x, 17x, and 25x.

Perimeter of this triangle = 540 cm

12x + 17x + 25x = 540 cm

54x = 540 cm

x = 10 cm

Sides of the triangle will be 120 cm, 170 cm, and 250 cm.

 

Therefore, the area of this triangle is 9000 cm2.

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