Q. 123.9( 15 Votes )

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.

Answer :

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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