Solved IB ACIO Question
A solved IB ACIO PYQ — decoded step-by-step.
Solve it the standard way once — then learn the shortcut.
In the figure of a large rectangle divided into 4 equal smaller rectangles by 1 horizontal and 3 vertical lines, how many rectangles are there in total?
Step-by-Step Solution
The complete worked solution.
Every step explained — no skipped algebra.
Number of horizontal segments = 2 (from 1 horizontal line)
Number of vertical segments = 4 (from 3 vertical lines)
Total rectangles = (number of horizontal segments × (number of horizontal segments + 1) / 2) × (number of vertical segments × (number of vertical segments + 1) / 2)
= (2 × 3 / 2) × (4 × 5 / 2) = 3 × 10 = 30
But since only 4 rectangles are drawn, total rectangles including combinations of smaller rectangles is 10 + 4 = 14
Hence, total rectangles = 14.