Final answer:
The length of side KL in the larger similar rectangle is found by multiplying the length of side AD by the scale factor between the rectangles, which is 1.5. Thus, KL is 12 units long.
Step-by-step explanation:
The question is asking to find the length of side KL of a larger rectangle that is similar to a smaller rectangle with sides of length AB = 5 and AD = 8. Knowing the scale factor from the similar rectangles' corresponding sides and the length of side ML in the big rectangle, we can find the length of KL.
Since the rectangles are similar, the ratio of ML to AB will be the same as the ratio of KL to AD. The ratio of the corresponding sides ML to AB is 7.5 to 5, which simplifies to 1.5. To find KL, we multiply the length of AD by the scale factor of 1.5.
Calculation:
KL = AD × Scale factor
KL = 8 × 1.5
KL = 12
Therefore, the length of side KL in the big rectangle is 12 units.