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Question
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.
Options
True
False
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Solution
This statement is True.
Explanation:
Since the sides of a triangle are a = 11 cm, b = 12 cm and c = 13 cm.
Now, semi-perimeter, `s = (a + b + c)/2`
= `(11 + 12 + 13)/2`
= `36/2`
= 18 cm
Area of a triangle = `sqrt(s(s - a)(s - b)(s - c))` ...[By Heron’s formula]
= `sqrt(18(18 - 11)(18 - 12)(18 - 13))`
= `sqrt(18 xx 7 xx 6 xx 5)`
= `sqrt(3 xx 6 xx 7 xx 6 xx 5)`
= `6sqrt(3 xx 7 xx 5)`
= `6sqrt(105)`
= 6 × 10.25
= 61.5 cm2
∴ Area of ΔABC = `1/2 xx BC xx AD` ...`[∵ "Area of triangle" = 1/2 ("base" xx "height")]`
= `1/2 xx 12 xx 10.25`
= 6 × 10.25
= 61.5 cm2
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