Each side of a pentagon is 10 cm greater than the previous side. If the perimeter of this pentagon is 500 cm, find the lengths of each side.
Let's assume the first side of the pentagon has length x cm.
The second side is x + 10 cm.
The third side is (x + 10) + 10 = x + 20 cm.
The fourth side is (x + 20) + 10 = x + 30 cm.
The fifth side is (x + 30) + 10 = x + 40 cm.
The perimeter of the pentagon is the sum of all the sides:
x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 500 cm.
Simplifying the equation:
5x + 100 = 500.
Subtracting 100 from both sides:
5x = 400.
Dividing both sides by 5:
x = 80.
So, the lengths of the sides of the pentagon are:
First side: x = 80 cm.
Second side: x + 10 = 80 + 10 = 90 cm.
Third side: x + 20 = 80 + 20 = 100 cm.
Fourth side: x + 30 = 80 + 30 = 110 cm.
Fifth side: x + 40 = 80 + 40 = 120 cm. Answer: \boxed{80,90,100,110,120}.
Two sides of a triangle are 5 and 55. Complete the inequality to show the possible lengths of the third side.
If the third side of the triangle is x, then __< x < __
In any triangle, the length of any side must be greater than the positive difference between the lengths of the other two sides and less than the sum of the lengths of the other two sides.
Given that two sides of the triangle are 5 and 55, we can complete the inequality as follows:
5 < x < 55 + 5.
Simplifying, we have:
5 < x < 60.
Therefore, the inequality that shows the possible lengths of the third side is 5 < x < 60.
NO!
Apologies for the mistake. Let's correct the inequality.
In a triangle, the length of any side must be greater than the positive difference between the lengths of the other two sides and less than the sum of the lengths of the other two sides.
Given that two sides of the triangle are 5 and 55, let's say the length of the third side is x. We can set up the inequality as follows:
55 - 5 < x < 55 + 5.
Simplifying, we have:
50 < x < 60.
Therefore, the correct inequality that shows the possible lengths of the third side is 50 < x < 60.
Let's assume the length of the first side of the pentagon is x cm.
Given that each side is 10 cm greater than the previous side, we can determine the lengths of the remaining sides.
The second side would be x + 10 cm.
The third side would be (x + 10) + 10 = x + 20 cm.
The fourth side would be (x + 20) + 10 = x + 30 cm.
The fifth side would be (x + 30) + 10 = x + 40 cm.
To find the perimeter, we add up the lengths of all sides:
x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 500
Now, let's solve this equation for x:
5x + 100 = 500
Subtract 100 from both sides:
5x = 400
Divide both sides by 5:
x = 80
Therefore, the lengths of the sides of the pentagon are:
First side: x = 80 cm
Second side: x + 10 = 90 cm
Third side: x + 20 = 100 cm
Fourth side: x + 30 = 110 cm
Fifth side: x + 40 = 120 cm
To solve this problem, we can set up an equation using the given information and solve for the lengths of the sides.
Let's assume the length of the first side of the pentagon is "x" cm.
According to the given information, each side of the pentagon is 10 cm greater than the previous side. So, the second side will be (x + 10) cm, the third side will be (x + 20) cm, and so on.
Now, let's calculate the perimeter of the pentagon by adding up all the side lengths:
Perimeter = x + (x + 10) + (x + 20) + (x + 30) + (x + 40)
According to the problem, the perimeter is 500 cm:
500 = x + (x + 10) + (x + 20) + (x + 30) + (x + 40)
To solve this equation, we combine like terms:
500 = 5x + 100
Subtract 100 from both sides:
400 = 5x
Divide both sides by 5 to solve for x:
x = 80
The length of the first side of the pentagon is 80 cm.
Now, we can find the lengths of the remaining sides by adding 10 cm to each previous side length:
Second side: x + 10 = 80 + 10 = 90 cm
Third side: x + 20 = 80 + 20 = 100 cm
Fourth side: x + 30 = 80 + 30 = 110 cm
Fifth side: x + 40 = 80 + 40 = 120 cm
Therefore, the lengths of each side of the pentagon are as follows:
First side: 80 cm
Second side: 90 cm
Third side: 100 cm
Fourth side: 110 cm
Fifth side: 120 cm