Question

In the adjoining figure,
seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.

Answer 1

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