A rectangular pool has a perimeter of 142 feet. The length is 25 feet longer than the width. Find the length and width of the pool.
P = 2L + 2W
142 = 2(W + 25) + 2W
142 = 4W + 50
92 = 4W
23 = W
To solve this problem, let's assign variables to represent the width and length of the pool.
Let's say:
Width = W
Length = L
According to the problem, the length is 25 feet longer than the width. Therefore, we can write the equation:
L = W + 25 (Equation 1)
Now, the perimeter of a rectangle is the sum of all its sides.
Perimeter = 2 × Length + 2 × Width
For this rectangular pool, the perimeter is given as 142 feet. So we can write the equation:
2L + 2W = 142 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (L and W). We can solve this system to find the values of L and W.
Let's substitute the value of L from Equation 1 into Equation 2:
2(W + 25) + 2W = 142
2W + 50 + 2W = 142
4W + 50 = 142
4W = 142 - 50
4W = 92
Dividing both sides by 4, we find:
W = 92 / 4
W = 23
Substituting this value of W back into Equation 1:
L = 23 + 25
L = 48
Therefore, the width of the pool is 23 feet and the length is 48 feet.