In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm. Is the given statement true or false and justify your answer.
Solution:
Given, the sides of a triangle are 11 cm, 12 cm and 13 cm
The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.
We have to determine if the given statement is true or false.
By Heron’s formula,
Area of triangle = √s(s - a)(s - b)(s - c)
Where s= semiperimeter
s = (a + b + c)/2
So, s = (11 + 12 + 13)/2
= 36/2
s = 18 m
Now, area = √18(18 - 11)(18 - 12)(18 - 13)
= √18(7)(6)(5)
= √6 × 3 × 7 × 6 × 5
= 6√3 × 7 × 5
= 6√105
= 6(10.25)
= 61.5 cm²
Area of triangle = 1/2 × base × height
In triangle ABC,
Area = 1/2 × BC × AD
61.25 = 1/2 × 12 × AD
61.25 = 6 × AD
AD = 61.25/6
AD = 10.25 cm
Therefore, the given statement is true.
✦ Try This: Find the area of a triangle whose sides are 34 cm, 20 cm and 42 cm . hence the length of the altitude corresponding to the shortest side.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12
NCERT Exemplar Class 9 Maths Exercise 12.2 Problem 9
In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm. Is the given statement true or false and justify your answer.
Summary:
The given statement “In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm” is true
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