Algebra Help?

Question

The length of a rectangle exceeds its width by 4 feet. If the width is doubled and the length decreased by 2 feet, a new rectangle is formed whose perimeter is 8 feet more than the perimeter of the original rectangle. Find the dimensions of the original rectangle.

Answer 1

L = W + 4,
P = 2L + 2W = 2(w+4) + 2W = 4W + 8

new rectangle, width is 2W, length is W + 4 - 2 = W + 2,
P = 2(W+2) + 2(2W) = 6W + 4

so 6W + 4 = 8 + 4W + 8
2W = 12
W = 6
L = 10

check, P = 2(10+6) = 32
new rectangle 8 by 12, P = 2(8+12) = 40, and 40 exceeds 32 by 8.

Answer 2

The length of a rectangle exceeds its width by 4 feet. If the width is doubled and the length decreased by 2 feet, a new rectangle is formed whose perimeter is 8 feet more than the perimeter of the original rectangle. Find the dimensions of the original rectangle.

Perimeter=2l+2w

So fill in the equations:
a. Original width is ___
b. Length in terms of width can be written: w + ___.
Original Perimeter would be 2w+2l.
So use the two equations above and fill in 2( )+2( ).

The new width is doubled so if the original width =w then the new width equals:
__ (w).
The old length was w+___, so if the new length is 2 feet less it equals w+___-___.

Using these two new equations in the Perimeter formula P=2l+2w and setting them equal to the Perimeter listed above add 8, gives
2(new width)+2(new length)=(old perimeter)+8.

If you solve this equation you will know the original width or w. And since you know w+4 is the length you can find the length as well. good luck!

Answer 3

Let the length of the rectangle = L (in feet)
Let the width of the rectangle = W (in feet)

The first statement gives us the equation: L = W + 4

For the second rectangle, the width is doubled (2W) and the length is decreased by 2 feet (L - 2). The perimeter of this rectangle, (let's call it P2) is 8 feet more than the perimeter of the original rectangle (let's call it P1)

Finding the perimeters is easy:
P1 = 2W + 2L
P2 = 2*2W + 2*(L-2) = 4W + 2L - 4

The second statement then, gives us the equation:
P1 + 8 = P2
2W + 2L + 8 = 4W + 2L - 4
2W + 8 = 4W - 4
8 + 4 = 4W - 2W
12 = 2W
W = 6

Using the first equation:
L = W + 4
L = (6) + 4
L = 10

Therefore, the length and width of the original rectangle are 10 feet and 6 feet, respectively.

Answer 4

let x be the width, then x + 4 is the length

P = 2(width + length)

perimeter of the original rectangle:
P = 2(x + x + 4)
P = 2(2x + 4)
P = 4x + 8

the length is increased by 2 ft
length: x + 4 + 2
length: = x + 6

the width doubles
width: 2x

the new perimeter of the new rectangle
P = 2(x + 2x + 6)
P = 2(3x + 6)
P = 6x + 12

the difference between the perimeter of the two rectanlge is 8

New - origion = 8

6x + 12 - (4x + 8) = 8
6x + 12 - 4x - 8 = 8
2x + 4 = 8
2x = 4
x = 2

so the dimention of the original rectangle is:
2ft x 6ft

edit: oops! i it say "decreased" but somehow i read it as "increased"

so the new length should be x + 4 - x = x + 2

so the answer should be like the answers belove me.

Answer 5

For increasing cubic binomials the final formulation is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 6

Is this a test? Because if it is you're cheating and that's horrible.