SOLUTION: A rectangular picture frame has a perimeter of 3 meters. the height of the frame is 2/3 times its with. (a)write H in terms of w and write an equation for the perimeter in terms o

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Question 945110: A rectangular picture frame has a perimeter of 3 meters. the height of the frame is 2/3 times its with.
(a)write H in terms of w and write an equation for the perimeter in terms of w.
(b)Find the dimensions of the picture frame
Answer by nerdybill(7384) About Me  (Show Source):
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A rectangular picture frame has a perimeter of 3 meters. the height of the frame is 2/3 times its with.
(a)write H in terms of w and write an equation for the perimeter in terms of w.
.
if w=width
then
height = (2/3)w
.
2(width+height) = perimeter
2(w + (2/3)w) = 3
(b)Find the dimensions of the picture frame
2(w + (2/3)w) = 3
divide both sides by 2:
(w + (2/3)w) = 3/2
multiplying both sides by 3:
3w + 2w = 9/2
5w = 9/2
w = 9/10 meters
.
height is:
(2/3)w = (2/3)(9/10) = (2)(3/10) = 3/5 meters