1.

The base of an isosceles triangle measures 24 cm and its area is `192 cm^(2)` , Find its perimeter.

Answer» Here , base ,b=24 cm am and let each equal side be a cm . Then ,
`area =(1)/(4)b sqrt(4a^(2)-b^(2))sq " units"=(1)/(4) xx24xxsqrt(4a^(2)-576)cm^(2)`
`= 12xxsqrt(a^(2)-144)cm^(2),`
`"but area " =192 cm^(2) ["given "]`.
`therefore 12xxsqrt(a^(2)-144)=192implies sqrt(a^(2)-144)=16`
`implies a^(2) -144 = 256implies a^(2) = 400 implies a=20.`
`therefore ` perimeter of the triangle `=(2a+b)cm `
`=(2xx20 +24)cm =64 cm.`


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