Question

The length y of a rectangle if four less than three time the width of x. The perimeter of the rectangle is 16cm. Write a system of equations to represent this situation and find the dimensions of the rectangle. please explain reasoning

Answer 1

To find the dimensions of the rectangle, we set up a system of equations representing the given information. By solving the system of equations, we find that the dimensions of the rectangle are 3cm and 5cm.

Step-by-step explanation:

To represent the situation, we can set up a system of equations. Let's say the length of the rectangle is y and the width is x.

The first equation states that the length y is four less than three times the width x:

y = 3x - 4

The second equation represents the perimeter of the rectangle, which is given as 16cm:

2x + 2y = 16

To find the dimensions of the rectangle, we can solve this system of equations. We can substitute the value of y from the first equation into the second equation:

2x + 2(3x - 4) = 16

Simplifying, we get:

2x + 6x - 8 = 16

Combining like terms:

8x - 8 = 16

Adding 8 to both sides:

8x = 24

Dividing both sides by 8:

x = 3

Substituting this value back into the first equation, we can find the value of y:

y = 3(3) - 4 = 9 - 4 = 5

Therefore, the dimensions of the rectangle are x = 3cm and y = 5cm.