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Question
The sides of a triangle are in the ratio 15 : 13 : 14 and its perimeter is 168 cm. Find the area of the triangle.
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Solution
Perimeter of the triangle = 168 cm
Sum of ratio of sides = 15 + 13 + 14 = 42
Let the first side =`(168xx15)/42` = 60 cm
Second side =`(168xx13)/42` = 52 cm
Third side =`(168xx14)/42` = 56 cm
Now, s =`"a + b + c"/2`
= `(60+52+56)/2=168/2=84`
∴ Area =`sqrt("s"("s"-"a")("s"-"b")("s"-"c"))`
= `sqrt(84(84-60)(84-52)(84-56))`
= `sqrt(84xx24xx32xx28)`
= `sqrt(2×2×3×7×2×2×2×3×2×2×2×2×2×2×2×7)`
= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7
= 1344 cm2
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