Assertion: The area of a triangle of sides 25 cm, 17 cm and 12 cm is 90 cm2 . The length of the altitude on the longest side is equal to 8.2 cm. Reason: If the base and area of a triangle is given, then its altitude can be calculated by using the formula, A = ½ x b x h.
Answers
Answer:
Semiperimeter is given by -
s = (a + b + c)/2
= (25 + 17 +12) / 2 S =
s = 27 cm
Area of triangle is calculated by -
Area of triangle = √[s (s-a) (s-b) (s-c)]
Area of triangle = √[27 (27-25) (27-17) (27-12)]
Area of triangle = 90 cm^2
Let h be altitude of longest side.
Area of triangle = 1/2 × b × h
90 = 1/2 x 25 x h
h = 90/12.5
h = 7.2 cm
◆ Answer -
h = 7.2 cm
● Explaination -
Semiperimeter is given by -
s = (a + b + c) / 2
s = (25 + 17 + 12) / 2
s = 27 cm
Area of triangle is calculated by -
Area of triangle = √[s (s-a) (s-b) (s-c)]
Area of triangle = √[27 (27-25) (27-17) (27-12)]
Area of triangle = 90 cm^2
Let h be altitude of longest side.
Area of triangle = 1/2 × b × h
90 = 1/2 × 25 × h
h = 90 / 12.5
h = 7.2 cm
Hence, altitude of longest side is 7.2 cm.
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