the width of a rectangle is one half its length. the perimeter of the rectangle is 54cm. what are the width and length of the rectangle.
let x be the length
let y be the width
y=1/2x
2x+2y=54
substitute-> 2x+2(1/2x)=54
2x+x=54
3x=54
x=18
since the width is half the length
18/2= 9
y=9
To solve this problem, we need to understand that the perimeter of a rectangle is the sum of all its sides. Given that the rectangle's width (W) is half its length (L) and the perimeter is 54 cm, we can set up an equation based on that information.
Step 1: Represent the given information with variables:
Let W be the width of the rectangle.
Let L be the length of the rectangle.
Step 2: Set up the equation using the given information:
The perimeter of the rectangle is the sum of all its sides, which can be expressed as:
Perimeter = 2W + 2L
Since the width is one half of the length, we can represent this relationship with the equation:
W = (1/2)L
We are also given that the perimeter is 54 cm, so we can set up the equation:
54 = 2W + 2L
Step 3: Substitute the value of W obtained from the relationship:
Using the equation W = (1/2)L, we can substitute this value of W into our perimeter equation:
54 = 2((1/2)L) + 2L
Simplifying the equation:
54 = L + 2L
Combining like terms:
54 = 3L
Step 4: Solve for L:
To isolate L, divide both sides of the equation by 3:
L = 54 / 3
L = 18 cm
Step 5: Calculate the width:
Substitute the value of L back into the equation W = (1/2)L:
W = (1/2) * 18
W = 9 cm
Therefore, the width of the rectangle is 9 cm, and the length is 18 cm.