The Distance, d, across the lake is 26.25 feet.
Similar Triangles
When two triangles have all the corresponding angles equal to each other, then their sides are in a ratio.
Given to us,
AB = 8 feet,
BC = 15 feet,
BP = 6 feet,
PQ = d,
AP = AB + BP = 8 + 6 = 14 feet
In the figure, [tex]\triangle ABC \sim \triangle APQ[/tex]
[tex]\dfrac{BC}{AB}=\dfrac{PQ}{AP}[/tex]
[tex]\dfrac{15}{8}=\dfrac{d}{14}[/tex]
[tex]d = \dfrac{15\times 14}{8}[/tex]
[tex]d = 26.25[/tex]
Hence, the Distance, d, across the lake is 26.25 feet.
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