Question

sides of a triangle are in the ratio 15:14:20 and its perimeter is 490cm .find its area?​

Answer 1

Step-by-step explanation:

Let the sides of the triangle be 15x, 14x and 20x:-

Now, the formula for Perimeter of a scalene triangle is → Sum of all its sides

According to the question:-

→ 15x + 14x + 20x = 490 cm

→ 49x = 490

→ x = 490/49

→ x = 10 cm

Therefore, the sides of the given triangle are:-

• 1st Side = 15x = 15 × 10 cm = 150 cm (a)

• 2nd Side = 14x = 14 × 10 cm = 140 cm (b)

• 3rd Side = 20x = 20 × 10 cm = 200 cm (c)

Now, semi-perimeter of the given triangle is:-

→ s = 490/2

→ s= 245

Now, the formula for area of triangle is:-

Now, the formula for area of triangle is:-→ [√ {s (s-a) (s-b) (s-c) } ]

→ [√ {245 (245-150) (245-140) (245-200) } ]

→ [√ {245 × 95 × 105 × 45} ]

→ [√10,99,74,375]

→ 10,486.86 cm²

Therefore, the area of the given triangle is 10,486.86 cm².

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