Question
The perimeter of a triangle is 30 cm and its area is 30`cm^2` . If the largest side measures 13 cm , hen wha is the length of the smallest side of the triangle ?
Answer: Option C
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Let the smallest side be `x` cm.
then , other sides are 13 cm and (17 - `x`)cm.
Let a = 13, b = `x` and c = (17 - `x`), so s = 15.
`:.` Area = `sqrt(s (s - a) (s - b) (s - c))` = `sqrt(15 xx 2 xx (15 - x) (x - 2))`
`hArr 30 xx (15 - x) (x - 2)` =`(30)^2`
`hArr (15 - x) ( x - 2) = 30`
`hArr x^2 - 17x + 60 = 0`
`hArr (x - 12) (x - 5) = 0`
`hArr x = 12 or s = 5
`:.` smallest side = 5 cm.
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