Three sides of a triangle measure 3, 4, and 5. Solve for the length of the shortest side of a similar triangle whose longest side has a length of 20. (1 point)
Let's call the shortest side of the triangle with sides measuring 3, 4, and 5, "x".
In a similar triangle, the corresponding sides will be proportional.
So, we can write:
x/3 = y/20
Where "y" is the corresponding side of the similar triangle whose longest side has a length of 20.
To solve for "x", we can rearrange the equation:
x = (3/20) * y
We know that the longest side of the triangle with sides measuring 3, 4, and 5 is 5, so the longest side of the similar triangle with longest side measuring 20 will also be 20.
Therefore, we have:
5/3 = 20/y
Solving for "y", we find:
y = (3 * 20)/5 = 12
Now, substituting back into our earlier equation:
x = (3/20) * 12 = 36/20 = 9/5 = 1.8
Therefore, the length of the shortest side of the similar triangle is 1.8.
Are you sure?
Apologies for the incorrect response earlier. Let's recalibrate our approach.
If the sides of a triangle measure 3, 4, and 5, we can conclude that it is a right triangle. The Pythagorean theorem states that, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, using the Pythagorean theorem, we can verify that the sides 3, 4, and 5 do satisfy this equality: \(3^2 + 4^2 = 9 + 16 = 25 = 5^2\).
Now, since we are looking for the similar triangle, we know that the corresponding sides of similar triangles are proportional. Consequently, the shortest side of the similar triangle will be a fraction of the longest side.
Let's represent the shortest side of the similar triangle as "x". The corresponding side of the original triangle is 3, and the longest side of the original triangle is 5. The corresponding side of the similar triangle will be 20.
We can set up a proportion as follows:
\(\frac{x}{3} = \frac{20}{5}\)
Simplifying this equation:
\(x = 3 \cdot \frac{20}{5} = 12\)
Therefore, the length of the shortest side of the similar triangle is 12.