A rectangular field has a total perimeter of 128 feet. The width is 24 feet less than the length.
What are the dimensions of the field?
L = W + 24
2L + 2W = 128
Substitute W + 24 for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.
76
To find the dimensions of the rectangular field, we can use the information given in the problem.
Let's assume the length of the field is "L" feet.
According to the problem, the width is 24 feet less than the length, so the width can be represented as (L - 24) feet.
The perimeter of a rectangle is calculated by adding the lengths of all its sides.
In this case, the perimeter is given as 128 feet. So, we can set up the equation:
Perimeter = 2(Length + Width)
Substituting the values we have:
128 = 2(L + (L - 24))
Simplifying the equation, we get:
128 = 2(2L - 24)
Divide both sides of the equation by 2:
64 = 2L - 24
Add 24 to both sides of the equation:
88 = 2L
Divide both sides of the equation by 2:
L = 44
Now that we have the length, we can substitute this value back into the equation for the width:
Width = L - 24
Width = 44 - 24
Width = 20
Therefore, the dimensions of the field are 44 feet by 20 feet.