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प्रश्न
The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude ______.
पर्याय
`16sqrt(5)` cm
`10sqrt(5)` cm
`24sqrt(5)` cm
28 cm
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उत्तर
The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude `underlinebb(24sqrt(5) cm)`.
Explanation:
Given: The sides of a triangle area = 35 cm, b = 54 cm and c = 61 cm, respectively.
So, semi-perimeter of a triangle is:
`s = (a + b + c)/2`
= `(35 + 54 + 61)/2`
= `150/2`
= 75
Area of triangle = `sqrt(s(s - a)(s - b)(s - c))`
= `sqrt(75(75 - 35)(75 - 54)(75 - 61))`
= `sqrt(75 xx 40 xx 21 xx 14)`
= `sqrt(5 xx 5 xx 3 xx 2 xx 2 xx 2 xx 5 xx 3 xx 7 xx 7 xx 2)`
= `5 xx 3 xx 2 xx 2 xx 7sqrt(5)`
= `420sqrt(5)`
As know that,
Area of triangle ABC = `1/2` × Base × Altitude
`1/2` × 35 × Altitude = `420sqrt(5)`
Altitude = `(420sqrt(5) xx 2)/35`
Altitude = `24sqrt(5)`
Therefore, the length of altitude is `24sqrt(5)`.
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