The lengths of thesides of a triangle are in the ration 3:4:5 and its – InterviewSolution

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1.	The lengths of thesides of a triangle are in the ration 3:4:5 and its perimeter is `144 c mdot`Find the area of thetriangle and the height corresponding to the longest side.
Answer» On dividing 144 cm in the ratio 3:4:5 , we get `A=(144xx(3)/(12))cm = 36 cm , b=(144xx(4)/(12))cm = 48cm` `and C=(144xx(5)/(12))cm = 60 cm.` `therefore s=(1)/(2) (36+48+60)cm =72 cm ` `(s-a)=(72-36) cm =36 cm .` `(S-b) =(72-48) cm = 24 cm ` `and (s-c) =(72-60) cm = 12 cm .` (i) Area of the triangle `=sqrt(s(s-a)(s-b)(s-c))` `=sqrt(72xx36xx24xx12)cm^(2)` `=72xx12cm^(2)=864 cm^(2).` (ii) Let base = 60 cm and the corresponding height = h cm . `therefore 30h= 864implies h=(864)/(30)=28.8.` Longest side = 60 cm , corresponding height = 28.8 cm .

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