Question

original scaled copy
5 ?
3 6
4 8
what number can you multiply each original length by to get each length in the scaled copy?
(original triangle with sides 3, 4, 5; scaled copy triangle with side 6, 8, ?; and a number pad)

Explanation:

Step1: Analyze the scale factor

To find the scale factor, we can divide the length of the scaled copy by the original length. Let's take the first pair: original length is 3, scaled copy is 6. So the scale factor $k = \frac{6}{3} = 2$. Let's check with another pair: original length is 4, scaled copy is 8. $k = \frac{8}{4} = 2$. So the scale factor is 2.

Step2: Confirm with other sides

For the original length 5, the scaled copy length should be $5\times2 = 10$. Also, checking the other sides of the triangle: original height 3, scaled height 6 (3×2), original base 4, scaled base 8 (4×2), so the scale factor is consistent.

Answer:

2