help me please.
the perimeter of a rectangle is 120 inches. The length exceeds the width by 10 inches. Find the length and the width.
P = 2L + 2W
120 = 2(W + 10) + 2W
120 = 4W + 20
100 = 4W
? = W
Hi Mrs. Sue... I'm still confused with the final answer. Can you make it more simple for me to understand. Thanks.
100/4 = 25
The width is 25.
The length is 25 + 10 = 35
120 = (2 * 25) + (2 * 35)
120 = 50 + 70
Sure! Let's solve this problem step by step.
Step 1: Understand the problem
We are given that the perimeter of a rectangle is 120 inches and that the length exceeds the width by 10 inches. We need to find the length and the width of the rectangle.
Step 2: Define the variables
Let's denote the width of the rectangle as 'x' inches. Since the length exceeds the width by 10 inches, we can represent the length as (x + 10) inches.
Step 3: Formulate the equations
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this problem, the perimeter is 120 inches. Substituting the values, we have:
120 = 2((x + 10) + x)
Step 4: Solve the equation
To find the length and width, we need to solve the equation. Let's simplify it:
120 = 2(2x + 10)
120 = 4x + 20
Subtracting 20 from both sides, we get:
100 = 4x
Dividing both sides by 4, we have:
25 = x
So, the width of the rectangle is 25 inches.
Step 5: Find the length
We know that the length, (x + 10), so substituting the value of x, we get:
Length = 25 + 10 = 35 inches
Therefore, the length of the rectangle is 35 inches.
Step 6: Check the solution
To check if our solution is correct, we can calculate the perimeter using the obtained values:
Perimeter = 2(Length + Width) = 2(35 + 25) = 2(60) = 120 inches
Since the perimeter is indeed 120 inches, our solution is correct.
Therefore, the length of the rectangle is 35 inches, and the width is 25 inches.