Question 414234: Sarah purchased two picture frames. The perimeter of the larger frame is 240cm, and the perimeter of the smaller frame is 140cm. The height of the smaller frame is the same as the width of the larger frame, and the width of the smaller frame is 10cm less than the height of the smaller frame. Find the dimensions of the larger frame.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Sarah purchased two picture frames.
The perimeter of the larger frame is 240cm, and the perimeter of the smaller frame is 140cm.
The height of the smaller frame is the same as the width of the larger frame,
and the width of the smaller frame is 10cm less than the height of the smaller frame.
Find the dimensions of the larger frame.
:
Let w = width of the smaller frame
let h = height of the smaller frame
:
let W = Width of the larger frame
Let H = Height of the larger frame
:
Write an equation for each statement:
:
" The perimeter of the larger frame is 240cm,"
2H + 2W = 240
simplify, divide by 2
H + W = 120
:
"the perimeter of the smaller frame is 140cm. "
2h + 2w = 140
simplify, divide by 2
h + w = 70
:
"The height of the smaller frame is the same as the width of the larger frame,
h = W
:
"the width of the smaller frame is 10cm less than the height of the smaller "
w = h - 10
h = w + 10
:
we know:
h + w = 70
(w+10) + w = 70
2w = 70 - 10
w = 30
then
h = 30 + 10)
h = 40
The dimensions of the smaller frame 40 by 30
:
H + W = 120 (we know h = W)
H + 40 = 120
H = 120 - 40
H = 80
then
W = 120 - 80
W = 40
The dimensions of the larger frame 80 by 40
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