the length of a rectangle is 4cm more than the width of the rectangle. If you increase the length by 8cm and decrease the width by 4cm, the area will remained unchanged. Find the original dimensions
old width ----x
old length --- x+4
new width --- x-4
new length --- x+4 +8 =x + 12
x(x+4) = (x-4)(x+12)
x^2 + 4x = x^2 + 8x - 48
-4x = -48
x = 12
old rectangle is 12 by 16
for an area of 192
new rectangle is 8 by 24
for an area of 192
My answer is correct
(L-4)L=area=(L+8)(w-4)
(L-4)L=(L+8)(L-4-4)
L^2-4L=L^2-8L +8L-64 check that.
-4L=-64
solve for l, then W
To find the original dimensions of the rectangle, let's start by assigning variables to the unknowns. Let's say the width of the rectangle is represented by 'x' centimeters.
According to the given information, the length of the rectangle is 4 centimeters more than the width. So, the length would be represented by 'x + 4' centimeters.
We can first calculate the area of the original rectangle. The area of a rectangle is given by length multiplied by width. Therefore, the area is:
Original Area = Length * Width
= (x + 4) * x
= x^2 + 4x
Now, we are told that if we increase the length by 8 centimeters and decrease the width by 4 centimeters, the area remains unchanged. Let's calculate the new dimensions and area using this information.
New Length = (x + 4) + 8
= x + 12
New Width = x - 4
New Area = New Length * New Width
= (x + 12) * (x - 4)
= x^2 + 12x - 4x - 48
= x^2 + 8x - 48
Since the two areas (original and new) are equal, we can set up an equation:
Original Area = New Area
x^2 + 4x = x^2 + 8x - 48
Simplifying the equation:
4x = 8x - 48
4x - 8x = -48
-4x = -48
x = 12
Therefore, the original width of the rectangle is 12 cm. Using this information, we can find the original length:
Original Length = x + 4
= 12 + 4
= 16
So, the original dimensions of the rectangle are 12 cm (width) and 16 cm (length).