The longest side of the other triangle is 30.00 inches long. The correct option is D. 30.00
From the question,
The ratio of the side lengths for a triangle is exactly 9:12:15
And there is another triangle which is similar to this, the shortest side is 18 inches long.
Let the shortest sides of the triangles be a and the longest sides be c
Let the sides of the first triangle be a₁, b₁, and c₁
Then, for the first triangle, a₁ : b₁ : c₁ = 9:12:15
Let the sides of the second triangle be a₂, b₂, and c₂
The shortest side, a₂ of the second triangle is 18 inches
Then, for the second triangle, a₂ : b₂ : c₂ = 18 : b₂ : c₂
Now, since the triangles are similar
By similar triangle theorem, we have that
[tex]\frac{a_{1} }{a_{2} } =\frac{c_{1} }{c_{2} }[/tex]
∴[tex]\frac{9}{18}=\frac{15}{c_{2} }[/tex]
Then,
[tex]9 \times c_{2} = 15 \times 18[/tex]
Now, divide both sides by 9
[tex]c_{2} = \frac{15\times 18}{9}[/tex]
[tex]c_{2} = \frac{270}{9}[/tex]
[tex]c_{2} = 30.00[/tex]
Hence, the longest side of the other triangle is 30.00 inches long. The correct option is D. 30.00
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