The perimeter of a rectangle is 10 m. Twice the width is equal to one- half the length. Find the length and the width.
2 w = L/2
or L = 4 w
perimeter = 2(L+w)
= 2( 5 w) = 10 w = 10
so
w = 1
L = 4
How did u get 5
To find the length and width of the rectangle given the perimeter and the relationship between the width and length, we can set up a system of equations.
Let's denote the length of the rectangle as L and the width as W.
From the information provided, we know that the perimeter of the rectangle is 10 m. The formula for the perimeter of a rectangle is P = 2L + 2W, so we can write the equation as:
2L + 2W = 10
We are also given that twice the width is equal to one-half the length, which can be written as:
2W = (1/2)L
To solve this system of equations, we can use substitution or elimination method. Let's use substitution:
Rearrange the second equation to solve for L:
L = 4W
Substitute this value of L into the first equation:
2(4W) + 2W = 10
Simplify:
8W + 2W = 10
Combine like terms:
10W = 10
Divide both sides by 10:
W = 1
Now, substitute this value of W back into the second equation:
2(1) = (1/2)L
2 = (1/2)L
Multiply both sides by 2:
4 = L
So, the length of the rectangle is 4 m and the width is 1 m.