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Question
The sides of a triangle are 11 m, 60 m and 61 m. The altitude to the smallest side is
Options
11 m
66 m
50 m
60 m
Solution
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
`A = sqrt(s(s-a)(s-b)(s-c))`, where
`s = (a+b+c)/2`
We need to find the altitude to the smallest side
Therefore the area of a triangle having sides 11 m, 60 m and 61 m is given by
a = 11 m ; b = 60 m ; c = 61 m
`s = (a+b+c)/2`
`s = (11+60+61)/2`
`s = 132/2`
s = 66 m
`A = sqrt(66(66-11)(66-60)(66-61))`
`A = sqrt(66(55)(6)(5))`
`A = sqrt(108900)`
A = 330 m2
The area of a triangle having base AC and height p is given by
`" Area " (A) = 1/2 ("Base" xx "Height")`
`"Area " (A) = 1/2 (ACxx p ) `
We have to find the height p corresponding to the smallest side of the triangle. Here smallest side is 11 m
AC = 11 m
`330 = 1/2 (11 xx p)`
`330xx2=(11xxp)`
` p = (330xx2)/11
p = 60 m
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