Question

1. each side of an equilateral triangle s is multiplied by a scale factor of k to create equilateral triangle t. the length of each side of triangle t is smaller than the length of each side of triangle s. which of the following could be the value of k? (sat prep)

k=1
k=0
k=\frac{5}{6}
k=\frac{7}{6}

Explanation:

Step1: Understand the scale - factor concept

When a figure is scaled, if the scale factor \(k\) is between \(0\) and \(1\), the new figure (in this case, triangle \(T\)) is smaller than the original figure (triangle \(S\)).

Step2: Analyze each option

• For \(k = 1\): The two triangles (original and scaled) would be congruent (same size).
• For \(k=\frac{5}{6}\approx0.83\): Since \(0 <\frac{5}{6}<1\), triangle \(T\) (scaled triangle) is smaller than triangle \(S\) (original triangle).
• For \(k = 0\): The side - length of the new triangle would be \(0\), which is not a valid non - degenerate triangle.
• For \(k=\frac{7}{6}\approx1.17> 1\): The new triangle would be larger than the original triangle.

Answer:

\(k = \frac{5}{6}\)