The lengths of the sides of a triangle are in the ration 3:4:5 and its perimeter is `144 c mdot` Find the area of the triangle and the height corresponding to the longest side.

Explanation

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 .