A rectangle has a perimeter of 42 inches. The width of the rectangle is 3 inches less than
1/2 the length. What are the dimensions of this rectangle?
Write your answer in the form "width, length
The length of a rectangle is 3 inches less than twice its width. If the perimeter of the rectangle is 42 inches, find the dimensions of the rectangle.
length ---- x
width ---- (1/2)x - 3
2( x + x/2 - 3) = 42
x + x/2 - 3 = 21
(3/2)x = 24
x = 24(2/3) = 16
the length is 16
the with = (1/2)(16) - 3 = 5
check:
2(5) + 2(16) = 42
my answer is correct
To find the dimensions of the rectangle, we need to set up an equation using the information given.
Let's start by letting the length of the rectangle be represented by 'L' in inches. According to the question, the width of the rectangle is 3 inches less than half the length. So, the width 'W' can be expressed as:
W = (1/2)L - 3
The perimeter of a rectangle is given by the formula:
Perimeter = 2(L + W)
Substituting the values for width and length in terms of L, the equation becomes:
42 = 2(L + ((1/2)L - 3))
Simplifying this equation, we get:
42 = 2(L + 1/2L - 3)
42 = 2(3/2L - 3)
42 = 3L - 6
Adding 6 to both sides, we have:
48 = 3L
Dividing both sides by 3, we find:
L = 16
Now, we can substitute the value of L back into the equation for the width:
W = (1/2)(16) - 3
W = 8 - 3
W = 5
Therefore, the dimensions of the rectangle are 5 inches for the width and 16 inches for the length.