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.
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.
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
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.
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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