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}.
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.
5 answers
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 < __
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.
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.
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.
2 answers