The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. Write the ratios as fractions in simplest form.

The two figures are similar Find the ratios red to blue of the perimeters and of the areas Write the ratios as fractions in simplest form class=

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Answer:

Ratio of perimeters = [tex]\frac{3}{4}[/tex]

Ratio of areas = [tex]\frac{9}{16}[/tex]

Step-by-step explanation:

Thinking process:

The ratio of the parameters is given by the following:

[tex]ratio = \frac{length of side 1}{length of side 2}[/tex]

        =[tex]\frac{6}{8} \\= \frac{3}{4}[/tex]

The ratio of the areas is given by:

[tex]ratio = (\frac{length of side 1}{length of side 2}) ^{2}[/tex]

        = [tex](\frac{6}{8}) ^{2}[/tex]

        = [tex]\frac{36}{64}[/tex]

        = [tex]\frac{9}{16}[/tex]

The values of the fraction of the perimeter and the area of the triangles will be 3/4 and 9/16 respectively.

  • Perimeter of triangle 1 = 6cm + 6cm + 6cm = 18cm
  • Area of triangle 1 = 1/2 b × h = 1/2 × 6cm × 6cm = 18cm²

  • Perimeter of triangle 2 = 8cm + 8cm + 8cm = 24cm
  • Area of triangle 2 = 1/2 × 8cm × 8cm = 32cm²

The fraction of the perimeters will be:

= 18cm/24cm = 3/4

The fraction of the areas will be:

= 18cm²/32cm²

= 9/16

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