In the given similar triangles the length of the longest side of each triangle will be 66 and 18.
We have,
The longest side of a triangle is 12 more than 3 times the longest side of a similar triangle,
And,
The ratio of similitude = 11:3,
Now,
According to the question,
Let, Side of smaller triangle = x ,
So,
The side of larger triangle = 12 + 3x
So,
We know that in similar triangles, ratio of sides is equal,
i.e.
[tex]\frac{12+3x}{x} =\frac{11}{3}[/tex]
On solving we get,
3(12 + 3x) = 11x
i.e.
36 + 9x = 11x
Now,
11x - 9x = 36
i.e.
2x = 36
On solving we get,
x = 18,
i.e.
Side of smaller triangle = 18
So,
The side of larger triangle = 12 + 3x = 12 + 3 × 18 = 12 + 54 = 66
Hence we can say that in the given similar triangles the length of the longest side of each triangle will be 66 and 18.
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