To find the length of the shortest side of a triangle similar to the triangle with sides 3, 4, and 5, where the longest side has a length of 20, we can use the concept of ratios.
First, let's identify the sides of the original triangle:
- Longest side = 5
- Other sides = 3 and 4
In the similar triangle, the longest side is given as 20.
To find the scale factor (k) by which the sides of the original triangle are multiplied to get the sides of the similar triangle, we set up the ratio of the longest sides:
\[ k = \frac{\text{Longest side of similar triangle}}{\text{Longest side of original triangle}} = \frac{20}{5} = 4 \]
Next, we apply this scale factor to find the lengths of the other two sides of the similar triangle:
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For the side that originally measures 3: \[ 3 \times k = 3 \times 4 = 12 \]
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For the side that originally measures 4: \[ 4 \times k = 4 \times 4 = 16 \]
Now we have the lengths of the sides of the similar triangle:
- Side 1: 12
- Side 2: 16
- Longest side: 20
The shortest side of the similar triangle is the one that originally measured 3, which is now 12.
Thus, the length of the shortest side of the similar triangle is 12.