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प्रश्न
In the adjoining figure,
seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.
उत्तर
3AX = 2BX
∴`( AX)/(BX) = 2/3`
`therefore(AX+BX)/(BX)=3+2/3` ...................(By componando)
`therefore(AB)/(BX) = 5/3`
In ΔBCA and ΔBYX,
∠B ≅ ∠B
∠BCA ≅ ∠BYX ................. (Corresponding angles)
∴ ΔBCA ∼ ΔBYX ................. (A-A test of similarity)
∴ `(BA)/(BX)=(AC)/(XY)`
∴ `5/3 = (AC)/9`
∴ 3 × AC = 45
∴ AC = 15
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