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Question
Find the areas of the triangle whose sides are 42 cm, 34 cm and 20 cm. Also, find the height corresponding to the longest side.
Solution
Let the sides of the triangle be a=20cm , b=34 cm and C= 42cm Let s be the semi-perimeter of the triangle.
`s=1/2(a+b+c)`
`s=1/2(20+34+42)`
`s=48 cm`
Area of the triangle=`sqrt(s(s-a) (s-b)(s-c))`
⇒`sqrt(48(48-20)(48-34)(48-42))`
⇒`sqrt(48xx28xx14xx6)`
⇒`sqrt(112896)`
⇒`336cm^2 `
Length of the longest side is 42 cm.
Area of a triangle =`1/2xxbxxh`
⇒ `336=1/2xx42xxh`
⇒` 672=42h`
⇒`672/42=h`
⇒`h=16 cm`
The height corresponding to the longest side is 16 cm.
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