Question 624: I'm having some trouble with these problems. Please Help
1. The perimeter of a rectangular lot is 222 feet. if the length is 33 feet shorter than twice the width, write an equation and then find the length and width of the lot.
2. An 18 foot board is cut into three pieces. the second piece is four times as long as the first piece and the third is 2 feet longer than the first piece. write an equation and then find the lengths of the three pieces.
Thank you
Answer by AnlytcPhil(1810)   (Show Source):
You can put this solution on YOUR website! I'm having some trouble with these problems. Please Help
`
1. The perimeter of a rectangular lot is 222 feet. if the length is 33 feet
shorter than twice the width, write an equation and then find the length and
width of the lot.
`
Let the width be w. Then to write the expression for the width from the words
`
>>...the length is 33 feet shorter than twice the width...<<,
`
we begin with the words "twice the width" or 2w, and then we make it 33 feet
shorter by subtracting 33, which gives us
`
length = 2w-33
`
` ` ` ` ` ` ` ` 2w-33
` ` ` ` ` ` `|ŻŻŻŻŻŻŻŻŻ|
` ` ` ` ` ` w| ` ` ` ` |w
` ` ` ` ` ` `|_________|
` ` ` ` ` ` ` ` 2w-33
`
Perimeter = distance around the rectangle, or
`
Perimeter = left side + top side + right side + bottom side, or
`
` ` ` 222 = w + (2w-33) + w + (2w-33)
`
Can you solve that? Answer: w = 48, length = 2(48)-33 = 63
`
`
2. An 18 foot board is cut into three pieces. the second piece is four times as long as the first piece and the third is 2 feet longer than the first piece. write an equation and then find the lengths of the three pieces.
`
Let x = the length of the first piece. Then use the words:
`
>>...the second piece is four times as long as the first piece...<<
`
to write the expression 4x for the second piece. Then use the words:
`
>>...the third is 2 feet longer than the first piece...<<
`
to write the expression for the third piece as x + 2.
`
` ` ` ` ` ` ` x ` ` 4x ` ` x+2
` ` ` ` ` ` `|ŻŻ|ŻŻŻŻŻŻŻŻ|ŻŻŻŻ|
` ` ` ` ` ` ` ŻŻ ŻŻŻŻŻŻŻŻ ŻŻŻŻ
`
Now add these parts up and equate to 18 feet:
`
x + 4x + (x+2) = 18
`
Solve that and get x = 8/3 or 2 2/3 feet or 2 ft 8 inches.
`
So the first part is 2'8", the second is 10'8" feet, and the third is 4'8".
`
Edwin J
|
|
|
