SOLUTION: The sides of a triangle are 12,15, and 20.if the shortest side of a similar triangle is 3, find the length of the longest side of the triangle.

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Question 1132728: The sides of a triangle are 12,15, and 20.if the shortest side of a similar
triangle is 3, find the length of the longest side of the triangle.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of a triangle are 12,15, and 20.if the shortest side of a similar
triangle is 3, find the length of the longest side of the triangle.
The sides of the first triangle are 12,15, and 20.

Let the sides of the second (similar) triangle be 3,x, and y.

Then 12 is to 3 as 15 is to x,

12%2F3=15%2Fx

Cross multiply:

12%2Ax=15%2A3
12x=45
x=+45%2F12=15%2F4=3.75  <--middle-size side (we weren't asked
                             for this, but I thought I'd find it
                             anyway.)

Also, 12 is to 3 as 20 is to y,

12%2F3=20%2Fy

Cross multiply:

12%2Ay=20%2A3
12y=60
y=60%2F12=5   <--longest side

Edwin

Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.
Well trained student must MOMENTARILY recognize the similar right angled (3,4,5)-triangle, when he (or she) is given a (12,15,20) triangle.

(3,4,5) is the first Pythagorean triple . . .