Solve this problem plz...

A rectangle has an area of 288 cm square.if the width is decreased by 1cm and length is increased by 1 cm the area would decreasedby 3 cm square.fin the original dimension of the rectangle.

just write what they give you:

xy = 288
(x-1)(y+1) = xy-3

Now just solve for x and y, and you have 16 by 18.

Or, just list the factors of 288 and 285:

9x32, 12x24, 16x18
3x95, 5x57, 15x19

and it's easy to see which pairs work.

Let's assume the original width of the rectangle is x cm and the original length is y cm.

According to the given information, we can set up the following equation for the area of the rectangle:
xy = 288

If the width is decreased by 1 cm and the length is increased by 1 cm, the new width would be (x - 1) cm and the new length would be (y + 1) cm.

The new area of the rectangle can be expressed as:
(x - 1)(y + 1) = 288 - 3

Expanding the equation and simplifying, we have:
xy + x - y - 1 = 285
xy + x - y = 286

Now, we can substitute the value of xy from the first equation into the second equation:
288 + x - y = 286

Simplifying further, we get:
x - y = -2

From here, we can use trial and error or substitution to find the values of x and y that satisfy both equations.

By trying different values, we can find that x = 18 and y = 16 satisfy the equations.

Therefore, the original dimensions of the rectangle are 18 cm (width) and 16 cm (length).

To solve this problem, let's start by representing the original dimensions of the rectangle.

Let's assume the original width of the rectangle as 'w' and the original length as 'l'. As given, the area of the rectangle is 288 cm².

We know that the area of a rectangle is given by the formula:

Area = width * length

So, in our case, we have:

288 = w * l

Next, we are given that if we decrease the width by 1 cm and increase the length by 1 cm, the new area would decrease by 3 cm².

So, the new width would be 'w - 1' and the new length would be 'l + 1'. The new area is given by:

New Area = (w - 1) * (l + 1)

According to the problem, the new area is 3 cm² less than the original area. So, we can write the equation as:

(w - 1) * (l + 1) = 288 - 3

Simplifying the equation, we have:

(w - 1) * (l + 1) = 285

Now, we have two equations:

1. 288 = w * l (Equation 1)
2. (w - 1) * (l + 1) = 285 (Equation 2)

To solve these equations, we can use substitution or elimination method.

I will use the substitution method to solve this problem.

Let's solve Equation 2 for 'w' in terms of 'l':

From Equation 2: (w - 1) * (l + 1) = 285
Expanding: w * l + w - l - 1 = 285
Rearranging: w * l + w - l = 285 + 1
Combining like terms: w * l + w - l = 286
Rearranging: w * l + w = l + 286
Subtracting 'l' from both sides: w * l + w - l = l + 286 - l
Simplifying: w * l + w - l = 286
Collecting like terms: w * l + w - l = 286
Combining like terms: w * l + w - l = 286
Simplifying: w * l + w = 286 + l
Subtracting 'w' from both sides: w * l + w - w = 286 + l - w
Simplifying: w * l = 286 + l - w

Now, substitute the expression for 'w' from Equation 1 into the above equation:

288 = w * l
w = 288 / l

w * l = 286 + l - (288 / l)

Multiply both sides by 'l' to eliminate the fraction:

w * l² = 286l + l² - 288

Rearrange the equation:

w * l² - 286l - l² + 288 = 0

Now, we have a quadratic equation in terms of 'l'. We can solve this equation to find the value of 'l'.

With the given values, we have:

a = 1 (coefficient of l²)
b = -286 (coefficient of l)
c = 288

Using the quadratic formula:

l = (-b ± sqrt(b² - 4ac)) / (2a)

Plugging in the values:

l = (286 ± sqrt((-286)² - 4(1)(288))) / (2(1))

Now, calculate the value of 'l':

l = (286 ± sqrt(81796 - 1152)) / 2

l = (286 ± sqrt(80644)) / 2

l = (286 ± 284) / 2

l = (286 + 284) / 2 or l = (286 - 284) / 2

l = 570 / 2 or l = 2 / 2

l = 285 or l = 1

Now, we have two possible values for 'l': 285 and 1.

Substitute these values back into Equation 1 to find the corresponding values of 'w':

For l = 285:

288 = w * 285
w = 288 / 285
w = 1.01

For l = 1:

288 = w * 1
w = 288

So, the possible dimensions of the original rectangle are:

Width = 1.01 cm and Length = 285 cm
Width = 288 cm and Length = 1 cm