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The sides of triangle are in the ratio 5: 12: 13 and its perimeter is 180 cm. The area of triangle is ____ $c m 2$ .

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Detailed Solution

The sides of triangle are in the ratio 5: 12: 13 and its perimeter is 180 cm. The area of triangle is 1080

c m 2

.
Given the sides of triangle are in the ratio 5: 12: 13 and its perimeter is 180 cm.
Let the sides of triangle be 5x, 12x, 13x.
Perimeter of triangle is,= sum of all sides

⇒ 5 x + 12 x + 13 x = 180 ⇒ 30 x = 180 ⇒ x = 18030 ⇒ x = 6

Now side a is,

a = 5 × 6 ⇒ a = 30

Now side b is,

b = 12 × 6 ⇒ b = 72

Now side c is,

c = 13 × 6 ⇒ c = 78

The value of semi-perimeter (s) is,

s = 1802 ⇒ s = 90

Now using Heron’s formula,

A r e a = s (s − a) (s − b) (s − c)

⇒ A r e a = 90 (90 − 30) (90 − 72) (90 − 78) ⇒ A r e a = 90 × 60 × 18 × 12 ⇒ A r e a = 1166400 ⇒ A r e a = 1080 c m 2

The area of triangle is 1080

c m 2

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