The perimeter of an isosceles triangle A B C measures 11...

The perimeter of an isosceles triangle $A B C$ measures 11 units and its two equal sides measure 4 units. If triangle $A B C$ is
similar to triangle RST and triangle RST has a perimeter of 22 units, then find all the sides of triangle RST.

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Key Concepts

Scale Factor

The scale factor is the ratio that relates the corresponding side lengths of two similar figures. It is instrumental in scaling measures from one figure to another, particularly when dealing with perimeters or side lengths, as multiplying by the scale factor translates dimensions from the smaller figure to the larger one.

Triangle Similarity

Similar triangles maintain the same shape, meaning their corresponding angles are equal and their corresponding sides have proportional lengths. This concept is essential in establishing relationships between triangles, enabling one to derive unknown side lengths from known ratios.

Perimeter

The perimeter represents the total distance around a figure, calculated in a triangle by summing the lengths of all three sides. It is a fundamental property used to relate and compare geometric figures, especially when additional information is provided or when figures are similar.

Isosceles Triangle

An isosceles triangle has at least two sides of equal length, which confers certain symmetrical properties to its angles and sides. Recognizing a triangle as isosceles allows for more streamlined calculations in problems where some side lengths or angles are known.

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