Question:In the triangles ABC and XYZ, the angle A equals the angle Y and the angle B equal the angle X. Given that AB=6 cm, AC=4 cm, BC=7 cm and that XY=4 cm, find the lengths of XZ and YZ.
Answer Since `hat(A)=hat(B)` and `hat(B) = hat(X)` the angles C and Z are equal. Therefore the triangles `{("ABC"),("YXZ"):}` are similar. `:. (AB)/(YX)=(BC)/(XZ)=(AC)/(YZ)` `:. 6/4=7/(XZ)=4/(YZ)` `:. XZ=4 2/3 cm; YZ=2 2/3 cm`
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In the triangles ABC and XYZ, the angle A equals the angle Y and the angle B equal the angle X. Given that AB=6 cm, AC=4 cm, BC=7 cm and that XY=4 cm, find the lengths of XZ and YZ.