The length of the largest square is either 23 or 24.
The question is incomplete. Probably the following is your question.
Rectangle PQRS is divided into eight squares, as shown in the figure below. The side length of each shaded square is 10. What is the length of the largest squares?
A) 18
B) 24
C) 16
D)23
E) 25
What is a square?
Rectangles with equal sides and angles are called Squares.
How to solve it?
The side length of each shaded square is 10 which implies that the length QR is 30.
From the diagram, we can see that the side of the large square is longer than the two side lengths of the shaded squares. This means the side length of the large square must be more than 2×10 = 20.
Thus we can discard options (A) 18 and (C) 16 as answers.
Moreover, we can also see that the smallest square has a length of more than half of the length of the shaded square. That means it must be more than 5 but less than 10.
Thus we can conclude that the length of the largest square is less than 25 but more than 20.
Thus we can discard option (E) 25
Hence, the answer is either (B) 24 or (D)23.
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