The longest side of a triangle is 3 greater than the longest side of a similar triangle. If the ratio of similitude is 5:4, find the lengths of the longest

We can set this up as a proportion.

Let the longest side of the smaller triangle = x

Let the longest side of the larger triangle = x + 3

And they're in a 5:4 ratio

So we have

(x+3)/x = 5/4    Cross-multiply

4(x+3) = 5x

4x + 12 = 5x    Subtract 4x from both sides.

12 = x      And this is the longest side of the smaller triangle.

x + 3 = 15    And this is the longest side of the larger triangle.

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