# The length of the sides of a triangle is 5 cm, 12 cm, and 13 cm. Find the length of the perpendicular from the opposite vertex to the side whose length is 13 cm.

Given: Length of the sides of the triangle are 5 cm, 12 cm, and 13 cm

To Find: Length of the perpendicular from the opposite vertex to the side whose length is 13 cm.

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

Area of a right-angled triangle

Diagram:

Assumption:

Let the sides of the triangle be,

a = 5 cm

b = 12 cm

c = 13 cm

And the length of the perpendicular AD is p cm.

Explanation:

s = 15 cm

Area = 30 cm2

Now, we know that area of a right-angled triangle can also be calculated by another formula. Therefore,

Area = 1/2 × 13 × p

Now both the areas will be equal,

1/2 × 13 × p = 30

Hence, the length of the perpendicular is .

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