Ask Question
18 February, 17:30

While walking by a classroom, Linda sees two perfect squares written on a blackboard. She notices that their difference is her favorite number, 99. She also notices that there are exactly two other perfect squares between them. What is the sum of the two perfect squares on the blackboard

+3
Answers (2)
  1. 18 February, 17:33
    0
    549

    Step-by-step explanation:

    considering 'n²' to express first square on board.

    Remember 'n' is an integer

    Now expressing second square with (n+3) ² on the board.

    (Therefore, The other two perfect squares in between are (n+1) ² and (n+2) ².

    If asking for the difference that is 99:

    (n+3) ² - n² = 99

    Solving for n:

    n² + 6n + 9 - n² = 99

    6n + 9 = 99

    6n = 90

    n = 90/6

    n = 15

    So the perfect squares on the board are:

    n² = > 15² = 225

    (n+3) ²=> 18² = 324

    The difference between the above is 99

    and exactly two other perfect squares (16² = 256 and 17² = 289) are in between.

    Thus, the sum of the two perfect squares on the blackboard is,

    225 + 324 = 549
  2. 18 February, 17:47
    0
    15^2

    18^2
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “While walking by a classroom, Linda sees two perfect squares written on a blackboard. She notices that their difference is her favorite ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers