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A rectangle that meets those conditions can be worked out like so:

Let x and y be it's width and height respectively. Given the equations for the perimeter and area of a rectangle, we can say:

2x + 2y = 16

∴x + y = 8

xy = 15

∴ x = 15/y

∴ 15/y + y = 8

∴ 15 + y2 = 8y

∴ y2 - 8y + 15 = 0

∴ y2 - 8y + 16 = 1

∴ (y - 4)2 = 1

∴ y - 4 = 1

∴ y = 5

Now that we have y, we can plug it into one of our first equations to calculate x:

xy = 15

∴ x = 15/y

∴ x = 15/5 = 3

So the rectangle has a width of 3 and a height of 5

Another shape with that relationship would be a rhombus. We know that the sides of the rhombus will all be equal, so they will each be 16/4, or 4 units long.

l ≡ length of one side = 4

We also know that the area of a rhombus is equal to it's base times it's height. The base in this case will be the length of a side, 4, and we are given the area, 15. So we can say:

15 = 4h

∴ h = 15/4

where h is the height of the rhombus.

Now that we have it's base, height, and side length, we can work out it's angles. If drawn out in a graph, these numbers will give us a convenient right triangle to find the smaller angle in the rhombus (note that all angles here are in radians):

sin(α) = h/l

∴ sin(α) = 15/16

∴ α= sin-1(15/16)

∴ α ≈ 1.215375

To get the other angle, all you need to realize is that it will be equal to π - α :

β = π - α

∴ β ≈ 3.141593 - 1.215375

∴ β ≈ 1.926218

Q: Can you draw 2 different shapes with an area of 15 and a perimeter of 16?

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Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.

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There are an infinite number of triangles with different shapes that all have the same area.

To draw a shape with the same area and perimeter, decide what shape you want to draw, then take the equations for area and perimeter and make them equal, and then solve what the various side lengths have to be. For instance, the area of a square is L2 where L is the side length, and the perimeter of a square is Lx4 We want them equal, so L2=Lx4 Dividing both sides by L gives us L=4, so if I draw a square with side length 4, it will have the same area and perimeter.

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Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.

35

It depends on how long do you draw the shape example you can draw a 6cm square and you draw a 8cm square they are different . So it really depends on how the shape is measured.

Without going into detail at the moment, I'd have to say Yes it's possible. See the related question for thought process.

There are an infinite number of triangles with different shapes that all have the same area.

To draw a shape with the same area and perimeter, decide what shape you want to draw, then take the equations for area and perimeter and make them equal, and then solve what the various side lengths have to be. For instance, the area of a square is L2 where L is the side length, and the perimeter of a square is Lx4 We want them equal, so L2=Lx4 Dividing both sides by L gives us L=4, so if I draw a square with side length 4, it will have the same area and perimeter.

No, but I can tell you that an 8 x 8 square has an area of 64 and a perimeter of 32.

This browser is hopeless for drawing but consider the following two rectangles: a*b and (a+1)*(b-1). Their perimeter will be 2a+2b but unless a = b-1, their area will be different.

Yes.

Sure, honey. First, let's keep it simple. To calculate the perimeter of a square, you just need to multiply the length of one side by 4. So, if the side length is "s", the formula is 4s. As for the flowchart, draw a square with "s" labeled on one side, then an arrow pointing to a box that says "Perimeter = 4s". Done and done, darling.

Yes, draw a 2 x 7 rectangle.

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