SOLUTION: The width of a rectangle is 9 cm shorter than it's length. The perimeter of the rectangle is 40 cm. What are the length and width of the rectangle? And I don't know how this w

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Question 231412: The width of a rectangle is 9 cm shorter than it's length. The perimeter of the rectangle is 40 cm. What are the length and width of the rectangle?

And I don't know how this works so if you don't answer this one too that's okay;
The perimeter of an equilateral triangle is 4 times the perimeter of a regular hexagon. The length of a side of the triangle is 10 cm more than 6 times the length of a side of the hexagon. What is the perimeter of the triangle? What is the perimeter of the hexagon?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The width of a rectangle is 9 cm shorter than it's length.
The perimeter of the rectangle is 40 cm.
What are the length and width of the rectangle?
:
Let x = the width
then, since the length is 9 cm longer
(x+9) = the length
:
P = 2L + 2W = 40
so we have
2(x+9) + 2x = 40
2x + 18 + 2x = 40
2x + 2x = 40 - 18
4x = 22
x =
x = 5.5 cm is the width
and
5.5 + 9 = 14.5 = the length
:
Check solution:
2(14.5) + 2(5.5) =
29 + 11 = 40
:
:
Let 3t = perimeter of the triangle (1 side = t)
Let 6h = perimeter of the hexagon (1 side = h)
"The perimeter of an equilateral triangle is 4 times the perimeter of a regular hexagon."
3t = 4(6h)
3t = 24h
Simplify, divide by 3
t = 8h
"The length of a side of the triangle is 10 cm more than 6 times the length of a side of the hexagon."
t = 6h + 10
Replace t with 8h
8h = 6h + 10
8h - 6h = 10
2h = 10
h = 5 cm one side of the hexagon
and
t = 8(5)
t = 40 cm, one side of the triangle
:
What is the perimeter of the triangle?
3(40) = 120 cm
What is the perimeter of the hexagon?
6(5) = 30 cm
:
Checks out: Given the perimeter of triangle is 4 time perimeter of hexagon