The area of the rectangle approximated to 3 significant figures is [tex]\mathbf{11,700 $ mm^2}[/tex].
Recall:
- Area of a rectangle = length [tex]\times[/tex] width
- We are only given the radius of the three circles = 28 mm each
- We need to find the length and width of the rectangle.
To do this, see the image in the attachment below.
Referring to the image attached, you will understand how we derived the length and width of the rectangle.
- The width of the rectangle = [tex]28 + 28 + 28 + 28 = 112 $ mm[/tex]
- The length of the rectangle = [tex]28 + x + 28 = x + 56 $ mm[/tex]
- Find x using Pythagorean Theorem, which is:
[tex]x^2 = b^2 - a^2[/tex]
[tex]a = 28 $ mm\\\\b = 56 $ mm\\\\x = ?[/tex]
- Plug in the values and solve for x
[tex]x^2 = 56^2 - 28^2\\\\x^2 = 2,352\\\\x = \sqrt{2,352} \\\\x = 48.5$ mm[/tex]
Length of the rectangle = [tex]x + 56 $ mm\\\\[/tex]
[tex]= 48.5 + 56 $ mm\\\\= 104.5 $ mm[/tex]
- Area of the rectangle = length [tex]\times width[/tex]
[tex]= 104.5 \times 112\\\\= 11,704 $ mm^2[/tex]
- Therefore, the area of the rectangle to 3 significant figures will be approximately [tex]\mathbf{11,700 $ mm^2}[/tex]
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