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Medium|   Geometry|      
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Donnie84
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The figure above is made up of 4 squares. If a straight line segment w 20 Mar 2024, 12:45
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83% (01:16) correct 16% (02:12) wrong based on 6 sessions

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­The figure above is made up of 4 squares. If a straight line segment were to be drawn from A to B, it would have a length of \(8 \sqrt{2}\) units. What is the perimeter of the entire figure in units?

A. 20
B. 32
C. 40
D. 64
E. 80­
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C
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The figure above is made up of 4 squares. If a straight line segment w 26 Mar 2024, 09:17
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Donnie84

­The figure above is made up of 4 squares. If a straight line segment were to be drawn from A to B, it would have a length of 8 2^(1/2) units. What is the perimeter of the entire figure in units?

A. 20
B. 32
C. 40
D. 64
E. 80­
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­

I am not sure I understand the length. Is that 82^1/2 or 8*2^1/2. This is a weird one. Can you clarify pls?
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The figure above is made up of 4 squares. If a straight line segment w 26 Mar 2024, 10:42
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bb

Donnie84

­The figure above is made up of 4 squares. If a straight line segment were to be drawn from A to B, it would have a length of 8 2^(1/2) units. What is the perimeter of the entire figure in units?

A. 20
B. 32
C. 40
D. 64
E. 80­
­

I am not sure I understand the length. Is that 82^1/2 or 8*2^1/2. This is a weird one. Can you clarify pls?
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­Fixed Now!
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The figure above is made up of 4 squares. If a straight line segment w 12 Apr 2024, 16:09
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­This becomes a triangle which has the angles in the ratio of \(45:45:90\) or \(x:x:x\sqrt{2}\)

We do know this because the segment AB is \(8\sqrt{2}\)

which means that the other sides are 8

One side of a square is 4.

We want to know the perimeter of the shaded region which has 10 sides

\(4 \times 10 = 40\)

C is the answer
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The figure above is made up of 4 squares. If a straight line segment w 22 Jun 2024, 01:50
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Official Explanation

­Each square shares at least one side with another square. That means all of the squares have the same side length. Segment AB would pass through two of the squares, creating two isosceles right triangles in each square. Since each square is the same size, the hypotenuse of each of those triangles would be \(8\frac{\sqrt{2}}{2} = 4\sqrt{2}\) units.

Recall that with isosceles right triangles, the ratio of the side lengths is \(x:x:x\sqrt{2}\), with \(x\sqrt{2}\) representing the hypotenuse. That means the actual hypotenuse of \(4\sqrt{2}\) corresponds to \(x\sqrt{2}\), and x, representing one side of a square, is 4. There are 10 sides around the perimeter of the figure, so the entire figure has a perimeter of 10 × 4 = 40 units. (C) is the correct answer.

Answer: C
­