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Question

The two figures are similar.

  1. Find the value of x.
  2. Find the values of the ratios (red to blue) of the perimeters and of the areas.


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Solution

Step 1: Find the value of x.

Given, figures

When two figures are similar, then their corresponding sides are equal.

Using the property similar figures.

x10=148x=17.5

Step 2: Find the ratio of perimeter of figures.

Using property of similar figures.

PerimeteroffigureAPerimeteroffigureB=sidelengthoffigureAsidelengthoffigureB

So, the ratio of perimeter of figure (red to blue) is,

PerimeterofredfigurePerimeterofbluefigure=148=74

Step 3: Find the ratio of area of figures.

AreaoffigureAAreaoffigureB=(sidelengthoffigureAsidelengthoffigureB)2

So, the ratio of area of figure (red to blue) is,

Hence, the value of x is 17.5 and ratio of perimeter and area of figure (red to blue) are 74 and 4916 respectively.


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