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saw5 [17]
3 years ago
14

Which figure will tessellate the plane? A. regular pentagon B. regular decagon C. regular octagon D. regular hexagon

Mathematics
1 answer:
Harrizon [31]3 years ago
5 0
<h3>Answer: D. regular hexagon</h3>

A hexagon is composed of 6 congruent equilateral triangles. Each equilateral triangle has interior angle of 60 degrees. Adding 6 such angles together gets you to 360 degrees. So we've done one full rotation and covered every bit of the plane surrounding a given point. Extend this out and you'll be able to cover the plane. A similar situation happens with rectangles as well (think of a grid, or think of tiles on the wall or floor)

In contrast, a regular pentagon has interior angle 108 degrees. This is not a factor of 360, so there is no way to place regular pentagons to have them line up and not be a gap or overlap. This is why regular pentagons do not tessellate the plane. The same can be aside about decagons and octagons as well.

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A gardener has 520 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it doe
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The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet

<h3>What dimensions would guarantee that the garden has the greatest possible area?</h3>

The given parameter is

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Represent the shorter side with x and the longer side with y

One side of the garden is bordered by a river:

So the perimeter is:

P = 2x + y

Substitute P = 520

2x + y = 520

Make y the subject

y = 520 - 2x

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A = xy

Substitute y = 520 - 2x in A = xy

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Expand

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Differentiate

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520 - 4x = 0

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4x= 520

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Substitute x= 130 in y = 520 - 2x

y = 520 - 2 *130

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A = xy

This gives

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Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet

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its a

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