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In triangle ABC, the line BD is perpendi...

In triangle ABC, the line BD is perpendicular to AC.The area of triangle ABC is `40 cm^2`. BD = (x+1)cm , AD = (x+6)cm , CD = (x+2)cm

Text Solution

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Area of `Delta ABC(A) = 1/2**AC**BD`
`A = 1/2**(AD+DC)**BD = 1/2**((x+2)+(x+6))**(x+1)`
We are given, `A = 40 cm^2`
`:. 1/2**((x+2)+(x+6))**(x+1) = 40`
`=>1/2**(2x+8)**(x+1) = 40`
`=>(x+4)(x+1) = 40`
`=>x^2+5x-36 = 0`
`=>x^2+9x-4x-36 = 0`
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