Similar Triangles

  • From: Angela
  • Date: 28 December 1999
  • Subject: Similar Triangles

In a triangle RST, X lies on RS and Y lies on RT. XY is parallel to ST.
If XS = 5,   TY = 6   and   RS = 12,   find RT

Maths Help suggests:

A sketch of the triangle

A sketch of the triangle will help.   (right)

Assuming X is on side RS and Y is on RT,
we can place measurements as shown.

Notice that RXY and RST are similar triangles.
This means that the triangle RST is an enlargement of triangle RXY.

The scale factor is RS/SX or 12/5

This means that RT is 12/5 ×TY     so     RT = 6 × 12/5.

Length RT is 14.4 units.

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