A rectangle is 4 times as long as it is wide. A 2nd rectangle is 5centimeters longer and 2 centimeters wider than the first. what are the dimensions of the original rectangle?

Question

A rectangle is 4 times as long as it is wide. A 2nd rectangle is 5centimeters longer and 2 centimeters wider than the first. what are the dimensions of the original rectangle?

Answer 1

original:

width = x
length = 4x

new rectangle:
width = x+2
length = 4x + 5

nothing else is given to form any type of equation.

Your question cannot be answered, something is missing.

Answer 2

i'm sorry i left out one part. "A rectangle is 4 times as long as it is wide. A 2nd rectangle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 530 square centimeters greater than the first. What are the dimensions of the original rectangle?

Answer 3

To solve this problem, let's start by assigning some variables. Let's call the width of the first rectangle 'w' and the length 'l'.

Given that the length (l) is 4 times the width (w), we can write the equation:

l = 4w ----(equation 1)

Now, let's move on to the second rectangle. We are told that the second rectangle is 5 centimeters longer and 2 centimeters wider than the first rectangle. This means we can express the dimensions of the second rectangle as follows:

Width of the second rectangle = w + 2
Length of the second rectangle = l + 5

Since we know the relationship between the width and length of the first rectangle, we can substitute the value of 'l' from equation 1 into the expressions for the width and length of the second rectangle:

Width of the second rectangle = w + 2
Length of the second rectangle = 4w + 5

Now, based on this information, we can form another equation:

4w + 5 = l + 2 ----(equation 2)

Now, we have a system of equations (equation 1 and equation 2) to solve for the values of 'w' and 'l'.

Let's substitute the value of 'l' from equation 1 into equation 2:

4w + 5 = 4w + 2

By subtracting 4w from both sides of the equation, we get:

5 = 2

This equation is not possible, as it results in a contradiction. Therefore, there is no solution that satisfies the given conditions.

In conclusion, based on the given information, it is not possible to determine the dimensions of the original rectangle.