Suppose that the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 50 inches. The formula for the perimeter of a rectangle is P=2L+2W.
a) Set up an equation for the perimeter involving only L, the length of the rectangle.
B) Solve this equation algebraically to find the length of the rectangle. Find the width as well.
W = L - 5
50 = 2L + 2W
Substitute L - 5 for W in the second equation and solve for L. Put that value in the first equation to find W. Check by putting both values into the second equation.
To set up an equation for the perimeter involving only the length of the rectangle, we can use the given information:
Let's assume the length of the rectangle is L inches.
According to the given information, the width of the rectangle is 5 inches shorter than the length. So, the width of the rectangle can be represented as (L - 5) inches.
The formula for the perimeter of a rectangle is P = 2L + 2W.
Substituting the values, we get:
P = 2L + 2(L - 5)
Simplifying this equation will give us an expression for the perimeter involving only the length (L).
Now, let's solve this equation algebraically to find the length of the rectangle:
Given that the perimeter of the rectangle is 50 inches, we can set up the equation:
50 = 2L + 2(L - 5)
Simplifying this equation further, we get:
50 = 2L + 2L - 10
Combining like terms, we have:
50 = 4L - 10
We can isolate the term containing L by adding 10 to both sides:
50 + 10 = 4L
60 = 4L
To find the value of L, divide both sides by 4:
60/4 = L
L = 15
So, the length of the rectangle is 15 inches.
To find the width, substitute the value of L back into the equation for the width:
Width = L - 5
Width = 15 - 5
Width = 10
Therefore, the width of the rectangle is 10 inches.