In ΔXYZ, R and S are points on the sides XY and XZ respectively, such that RS is parallel to YZ. XR=15cm, XY=25cm, XS=12cm and XZ=20cm. RS is equal to:
- A5
2
YZ - B3
5
YZ - C5
3
YZ - D4
3
YZ
Solution & Step-by-step Explanation
In ΔXYZ, it is given that RS∥YZ.
By the property of similar triangles (specifically, ΔXRS∼ΔXYZ due to AAA similarity as ∠XRS=∠XYZ and ∠XSR=∠XZY), the ratio of corresponding sides is equal:
XY
XR
=
XZ
XS
=
YZ
RS
Let us compute the ratio using the given lengths:
XY
XR
=
25
15
=
5
3
Let's double check with the other side:
XZ
XS
=
20
12
=
5
3
Equating this to the third side ratio:
YZ
RS
=
5
3
⟹RS=
5
3
YZ
By the property of similar triangles (specifically, ΔXRS∼ΔXYZ due to AAA similarity as ∠XRS=∠XYZ and ∠XSR=∠XZY), the ratio of corresponding sides is equal:
XY
XR
=
XZ
XS
=
YZ
RS
Let us compute the ratio using the given lengths:
XY
XR
=
25
15
=
5
3
Let's double check with the other side:
XZ
XS
=
20
12
=
5
3
Equating this to the third side ratio:
YZ
RS
=
5
3
⟹RS=
5
3
YZ