math help please ?!?

Question

a rectangle is 4 cm longer than it is wide. If the length and width are both decresed by 2 cm the area is decreased by 24 cm squared. find the dimensions of the original rectangle.

Please show your steps i'm very confused

Answer 1

Let x equal the width of the rectangle and y equal the area
1. y = (x)(x+4) [area of rectangle equals length times width]
2. y - 24 = (x-2)(x+2) [length and width decreased by 2 cm]
Substitute 1 into 2
(x)(x+4) - 24 = (x-2)(x+2)
x squared + 4x - 24 = x squared - 4
x squared - x squared + 4x = 24 - 4
4x = 20
x = 5
Therefore, the width is 5 cm and the length is 9 cm

Answer 2

let x be the width of the original rectangle

original length = x + 4
original width = x
original area = x(x + 4)

new length = x + 2
new width = x - 2
new area = (x + 2)(x - 2)

difference in the area of the original and new rectangle = original area - new area
24 cm = (x)(x + 4) - (x + 2)(x - 2)
24 cm = 4x + 4
24 cm = 4(x + 1) ----- (divide by 4)
6 cm = x + 1
x = 5 cm

therefore, original dimension is 5 cm x 9 cm
length = 9 cm
width = 5 cm

Answer 3

Let x= width of original rectangle
Then x+4 = width of original rectangle
Area of original rectangle = x(x+4) = x^2 + 4x

x-2 = width of new rectangle
x+2 = length of new rectangle
Area of new rectangle =(x-2)(x+2) =x^2 -4

Area original - area new = 24, so
x^2+4x - (x^2-4) = 24
x^2 +4x -x^2 +4 = 24
4x=20
x=5 =original width
x+4 =5+4 = 9 = original length

Answer 4

let the length = a
wide = w
therefore, a = 4 + w
area = A
aw=A
(4+w)w=A
since length and width decrease 2 cm when area decrease 24 cm squared,
(a-2)(w-2)=A-24
(4+w-2)(w-2)=A-24
since A=(4+w)w
therefore (2+w)(w-2)=(4+w)w-24
w^2-4=4w+w^2-24
20=4w
w=5cm
and thus length, a= 9cm
original dimension is:
length=9cm
width=5cm
area=45cm squared

Answer 5

let a and b be the length and the width
we have
a = b+4
(a - 2) * (b-2) = ab - 24
<=> ab - 2(a+b) + 4 = ab - 24
<=> 2(a+b) = 28
<=> a + b =14
a - b = 4
=> a = 9 and b = 5

Answer 6

width = x
length = x + 4

The area of rectangle (y)
y = x (x+4)
y = x2 + 4x

The decreased area is
y - 24 = (x-2)((x+4)-2)
y - 24 = (x-2)(x+2)
y - 24 = x2 - 4
y = x2 - 4 + 24
y = x2 + 20

combine both y:
y = y
x2 + 4x = x2 +20
4x = 20
x = 5

length = 9 cm
width = 5 cm

Answer 7

w + 4 = l
a = wl = w(w + 4) = w^2 + 4w
a = (w - 2)(l - 2) + 24 = (w - 2)(w + 4 - 2) + 24 = (w - 2)(w + 2) + 24 = w^2 - 4 + 24 = w^2 + 20

So w^2 + 4w = w^2 + 20
4w = 20
w = 5

l = 5 + 4 = 9

Length 9cm, width 5 cm

Answer 8

An other method :
Think you cut a band on long side ans short side of your rectangle. The length of this band is

Long-side + (Short side - width of band) = 24cm^2/2 = 12cm
short side + 4cm + short side - 2cm = 12 cm
2 short sides = 10 cm
1 short side = 5 cm
long side = 9 cm

The advantage of this method is, that the steps can be easily done in head.

Answer 9

That's hard....I am stupid at Math.I can't help