a rectangle has a width of one less than the length . if the perimeter is 30 units , what is the length and width ?
I am having problems starting of the equation . I understand how to do it but have a hard time setting it up correctly.
P = 2L + 2W
P = 2L + 2(L - 1)
30 = 4L - 2
32 = 4L
8 = L
Let's assume the length of the rectangle is x units.
According to the given information, the width is one less than the length, which means the width is (x - 1) units.
The formula for the perimeter of a rectangle is given by P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is given as 30 units, so we can write the equation as:
30 = 2(x + (x - 1))
Simplifying the equation:
30 = 2(2x - 1)
30 = 4x - 2
Adding 2 to both sides of the equation:
30 + 2 = 4x
32 = 4x
Dividing both sides by 4:
32/4 = x
x = 8
So, the length of the rectangle is 8 units.
Substituting the value of x back into the equation for the width:
Width = (x - 1) = (8 - 1) = 7 units
Therefore, the length of the rectangle is 8 units and the width is 7 units.
To solve this problem, we need to set up equations based on the given information.
Let's denote the length of the rectangle as L and the width as W.
We know that the width is one less than the length, so we can write the equation: W = L - 1.
We also know that the perimeter of a rectangle is given by the formula: P = 2(L + W).
Substituting the value of W from the first equation into the second equation, we get: P = 2(L + (L - 1)).
Now we can substitute the given value of the perimeter (P = 30) into the equation: 30 = 2(L + (L - 1)).
Simplifying this equation gives us: 30 = 2(2L - 1).
Expanding the multiplication, we get: 30 = 4L - 2.
Adding 2 to both sides gives us: 32 = 4L.
Dividing both sides by 4 gives us: L = 8.
Now we can substitute the value of L back into the first equation to find the width: W = L - 1 = 8 - 1 = 7.
Therefore, the length of the rectangle is 8 units, and the width is 7 units.