The length of a side of a pentagon is 69 units.
Since the hexagon on the left has 6 sides, and all of the sides have an equal length, if you multiply the number of sides(6) by the length of one side (3x+5) you will get the perimeter of the hexagon, 6(3x+5)
This is the same for the pentagon as well, since the pentagon on the right has 5 sides, and all of the sides have an equal length, if you multiply the number of sides(5) by the length of one side (4x-1) you will get the perimeter of the pentagon, 5(4x-1)
Now we have the equation for the perimeter of the hexagon, 6(3x+5), and the pentagon 5(4x-1). Since we know that the perimeters are the same length for each shape, we can set these two formulas equal to each other
Here is how I set up my equation
6(3x+5)=5(4x-1)
Now that you have the equation, you must solve for x, which I will demonstrate the steps down below
6(3x+5)=5(4x-1)
18x+30=20x-5 (subtract 18x on both sides)
30=2x-5 (subtract -5 on both sides)
35=2x (divide 2 on each side)
17.5=x
Now that you have determined that x is 17.5, all that is left to do is plug in 17.5 into the equation that solves for one side of the pentagon(4x-1) to get the length of a side of a pentagon, which is your answer.
Here is the work if needed
4(17.5)-1
70-1
69
The length of a side of a pentagon is 69 units.
I hope this helped!
Leave a comment on my answer if you have any questions on what I said here or need any more help with math.
If a circle has center (a,b) and radius r, the equation is
So, you have
Answer:
Commutative property of addition
Step-by-step explanation:
This is called the commutative property of addition which states that a + b = b + a. In this case, a = 3 and b = 7.
Answer: D. SSS
Step-by-step explanation:
The solution would be SSS because the image shows that AB is congruent to DE, BC is congruent to EF, and AC is congruent to DF. Because the image shows that all three sides are congruent to their corresponding side on the other triangle, with no mention of angles, the triangles are congreunt through the SSS theorem.
Answer:
Area of the triangle = 6x3/2=18/2=9cm²
now find semicircle then add
area of the semicircle= πr²/2=π6²/2=36π/2=18π
now add and you get
Area of the region = (18π+9)cm²
Step-by-step explanation:
