3. The lengths of the sides of a triangle are 7cm , 13cm and 12cm. Find the length of
perpendicular from the opposite vertex to the side whose length is 12cm.
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ANSWER :
4.89897948
BY HERON FORMULA
a, b, and c are the three sides of a triangle, then its area is,
Area = √[s(s-a)(s-b)(s-c)]
Here, "s" is the semi-perimeter of the triangle, i.e.,
s = (a + b + c)/2.
= (12+13+7)/2
= 16
A = √[s(s-a)(s-b)(s-c)]
= √[16(16-12)(16-13)(16-7)]
= √[8 × 4 × 3 × 9]
= √(864)
≈ 29.3938769
the perpendicular from vertex is called as altitude
now altitude at base b
L = 2 × area / base
= 2 × 29.3938769 /12
= 4.89897948
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