Similar triangles sides are in ratio. The distance between the penguins and the stingrays is 28 feet.
Similar triangles are the triangles whose corresponding sides are in ratio and the corresponding angles are of the same measurement.
As it is given that the length of the sides of the triangle with points as whales, sharks, and dolphins, the distance from whales to sharks is 18 feet and whales to dolphins is 27 feet. Also, In the triangle with points dolphins, stingrays, and penguins. The distance from dolphins to stingrays is 42 feet and from stingrays to penguins is x feet.
Further, if we draw the diagram according to the given conditions, then, we will get the diagram as shown below. In the two of the given triangles,
ΔABD and ΔDPS
The line AB and PS are parallel to each other,
The line AD and DS are part of the same line AS, and
The line BD and DP are part of the same line.
Therefore, using the SSS property for similar triangles. we can say that the ΔABD and ΔDPS are similar triangles.
In similar triangles, the corresponding sides are in the ratio, therefore, if we keep the ΔDBA on the ΔDPS, then they should look alike. Therefore, the ratio of the sides can be written as,
[tex]\dfrac{AD}{DS}=\dfrac{AB}{PS}[/tex]
Substituting the values we will get,
[tex]\dfrac{27}{42}=\dfrac{18}{x}\\\\x= \dfrac{18 \times 42}{27}\\\\x = 28\rm\ feet[/tex]
Hence, the distance between the penguins and the stingrays is 28 feet.
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