Seven squares with side lengths 1, 2, 2, 2, 3,
4, and 5 units are fit together without any
gaps or overlaps, to form a rectangle. What
is the shorter side length of the rectangle?
Answers
Given :-
- Seven squares with side lengths 1, 2, 2, 2, 3,
- 4, and 5 units are fit together without any
- gaps or overlaps, to form a rectangle.
To find :-
- What is the shorter side length of the rectangle ?
Solution :-
it has been given that, their is no gap between the squares, ans they are not overlapping .
Suppose if we assume that , first we put square with smallest side that is 1 unit. Than on right or left we start putting rest squares in increasing order. (Lets assume on right side .)
→ 1 unit → 2 unit → 2 unit → 2 unit → 3 unit → 4 unit → 5 unit . { with no gap} .
Than,
→ on Bottom , Total side Length becomes = 1 + 2 + 2 + 2 + 3 + 4 + 5 = 19 units. = Larger side of the rectangle.
Now,
when we see on right most side , we have largest square with units is their.
Therefore,
if we want to make a boundry along the new figure so formed , (rectangle) , we must need our breadth to be 5 units, so the right most Square can fit exactly without any gap .
Hence,
we can conclude that, The shorter side length of the rectangle is 5 units.
Answer:
7 is the ans...
Step-by-step explanation:
(1×1)+(2×2)+(2×2)+(2×2)+(3×3)+(4×4)+(5×5)= 63
63= area of the rectangle
63 ÷ 9 (one of its factors)
=7
they both are sides 9×7= 63
7<9 hence, proven...