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The sides of the triangle are in the ratio 5: 12 :13 and its perimeter is 150 cm. The area of the triangle is ____ $c m 2$ .

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Detailed Solution

The sides of the triangle are in the ratio 5: 12 :13 and its perimeter is 150 cm. The area of the triangle is 750

c m 2

.
Given the sides of the triangle are in the ratio 5: 12 :13 and its perimeter is 150 cm.
Let the sides equal to 5k, 12k, 13k.
The perimeter of triangle = sum of all sides

⇒ 150 = 5 k + 12 k + 13 k ⇒ 150 = 30 k ⇒ k = 5

The sides are

5 × 5, 12 × 5, 13 × 5

.
The sides are 25, 60 and 65.
Now the value of s is,

s = a + b + c 2 ⇒ s = 25 + 60 + 65 2 ⇒ s = 1502 ⇒ s = 75

Now, area of triangle using Heron’s formula is,

A = s s − a s − b s − c ⇒ A = 75 75 − 25 75 − 60 75 − 65 ⇒ A = 562500 ⇒ A = 750 c m 2

The area of triangle is 750

c m 2

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