Solve system of equations to model the problem then solve:
The length of a rectangle is 7 inches more than the width. The perimeter is 34 inches. Find the length and the width of the rectangle.
P = 2L + 2W
34 = 2(W + 7) + 2W
he perimeter of a circuit board is 30.4 inches and the length of its diagonal is 11 inches. What are the dimensions of the circuit board?
To solve this problem, we will set up a system of equations based on the given information. Let's denote the width of the rectangle as "w" and the length as "l".
1) The first sentence tells us that the length of the rectangle is 7 inches more than the width:
l = w + 7
2) The second sentence states that the perimeter of the rectangle is 34 inches. The perimeter of a rectangle is calculated by adding all four sides:
2w + 2l = 34
Now we have a system of two equations with two variables. We can solve this system to find the values of "l" and "w".
Step 1: Substitute the value of l from equation (1) into equation (2):
2w + 2(w + 7) = 34
Step 2: Simplify and solve for "w":
2w + 2w + 14 = 34
4w + 14 = 34
4w = 34 - 14
4w = 20
w = 20/4
w = 5
Step 3: Substitute the value of "w" back into equation (1) to find "l":
l = w + 7
l = 5 + 7
l = 12
So, the length of the rectangle is 12 inches, and the width is 5 inches.