Find the area of a triangle whose sides are 12 cm, 15 cm and 20 cm. Then, find the
measure of altitude corresponding to the longest side.
Answers
Step-by-step explanation:
which is the required ans.
SOLUTION:-
➡️In order to find the altitude to the longest side of a triangle, first we have to find the area of the triangle.
S = (a + b + c) / 2
➡️Substitute 12 for a, 16 for b and 20 for c.
S = (12 + 16 + 20) / 2
S = 48/2
S = 24
➡️Formula for area of scalene triangle :
= √[s(s - a)(s - b)(s - c)]
➡️Substitute.
= √[24 x (24 - 12) x (24 - 16) x (24 - 20)]
= √(24 x 12 x 8 x 4)
= 96 cm²
➡️Because we want to find the altitude to the longest side, the longest side will be the base of the triangle as shown above
➡️Here, the longest side is 20 cm.
➡️Area of the above triangle = 96 cm²
(1/2) x 20 x h = 96
10h = 96
➡️Divide each side by 10.
h = 9.6 cm
➡️So, the altitude to the longest side is 9.6 cm.
