# Length of three altitudes of a triangle are 3 cm, 4 cm and 5 cm. Find

| Length of three altitudes of a triangle are 3 cm, 4 cm and 5 cm. Find perimeter of triangle.

A.

B.

C.

D.

### Right Answer is: B

#### SOLUTION

Let BC =a, AB = c, AC =b

Also AD= =3cm , CE= h_{3} = 5 cm , BF = h_{2} = 4 cm

⇒

So sides of triangle 20x, 15x, 12x

Now by Heron’s formula

Area of triangle = , where s is the semi- perimeter

Here s = ( 20x + 15x + 12x )/ 2 = 47x/2

Area of triangle is also given by = (1/2)(20x)(3) = 30x

So perimeter of triangle = 20x + 15x + 12x = 47x

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Length of three altitudes of a triangle are 3 cm, 4 cm and 5 cm. Find