Mathematics

Question

Triangles EFG and QRS are similar. The lengths of the sides of EFG are 72, 64, and 56. The length of the smallest side of QRS is 140, what is the length of the longest side of QRS?

2 Answer

  • The longest side in the triangle is 180, as you multiply 18 by 10.

    Hope I helped!
  • Answer:

    [tex]180\ units[/tex]

    Step-by-step explanation:

    we know that

    If triangles EFG and QRS are similar

    then

    the scale factor is equal to the measure of the smallest side of triangle QRS divided by the smallest side of triangle EFG

    so

    Let

    x-------> the smallest side of triangle QRS

    y-------> the smallest side of triangle EFG

    z-------> the scale factor

    we have

    [tex]x=140\ units, y=56\ units[/tex]

    substitute the values

    [tex]z=\frac{140}{56}[/tex]

    [tex]z=2.5[/tex]

    Find the length of the longest side of QRS

    The length of the longest side of QRS is equal to multiply the scale factor by the length of the longest side of EFG

    so

    [tex]2.5*72=180\ units[/tex]

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