Asquare and a rectangle have the same perimeter. the square has a side length of 8x units. the rectangle has a length of (10x+8) units and a width of 10 units. what will be the perimeter of either the rectangle and the square?

Well we know that the perimeters are equal so:
Psquare = Prectangle

we know perimeter for square is the 4 sides of same lengths added up or 4*s

the perimeter of a rectangle is the then4 sides with 2 being equal added up so 2*L + 2*W

we know that a square side equAls s and it says that s=8x. So:
Psqu = 4 * (8x) (substitute 8x for s)

we know that the rectangle L =10x + 8 and W =10. So
Prect = 2 *(10x + 8) + 2 * (10)

we know :
Prect = Psqu so:
4 * (8x) =2 *(10x + 8) + 2 * (10)
32x = 20x + 16 + 20
12x = 36
x = 3

So if x equals 3 we can sub x in for square perimeter
Psqu = 4 *(8 * 3)
P = 4 * 24
P = 96

we can check this with rectangle perimeter
P = 2 *(10 * 3 + 8) + 2 *10
P = 2 * 38 + 20
P = 96

draw lines center to vertex

43.5 square inches

261 square inches

Step-by-step explanation:

Part A:

The area can be decomposed into triangles by drawing a line from the center to each vertex of the hexagon.

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Part B:

The area of each triangle is given by the triangle area formula:

 A = (1/2)bh

 A = (1/2)(10 in)(8.7 in) = 43.5 in²

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Part C:

The area of the table top is 6 times the area of one triangle:

 surface area = 6(43.5 in²) = 261 in²

Step-by-step explanation: