in the triangles abc and xyz angle a equals y b, Ratio And Percentage, Mathematics (O-Level)

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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.

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 ˆA=ˆBhat(A)=hat(B) and ˆB=ˆXhat(B) = hat(X) the angles C and Z are equal. Therefore the triangles {ABCYXZ{("ABC"),("YXZ"):} are similar. ∴ABYX=BCXZ=ACYZ:. (AB)/(YX)=(BC)/(XZ)=(AC)/(YZ) ∴64=7XZ=4YZ:. 6/4=7/(XZ)=4/(YZ) ∴XZ=423cm;YZ=223cm:. XZ=4 2/3 cm; YZ=2 2/3 cm

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. $:. (AB)/(YX)=(BC)/(XZ)=(AC)/(YZ)$ $:. 6/4=7/(XZ)=4/(YZ)$ $:. XZ=4 2/3 cm; YZ=2 2/3 cm$