the length of a rectangle is 25cm twice its width the perimeter of the table must be less than 335 cm.find the maximum dimensions of the table if each dimension is an interger
width --- x
length -- 2x
2x + 2(2x) < 335
6x < 335
x < 55.8
but we can't go over 335 and x must be an integer, so
x = 55
width = 55
length = 110
check:
if w=55, l = 110 , Perimeter = 330 < 335
if w = 56, l = 112, Perimeter = 336 > 335 , no good
To find the maximum dimensions of the table, we need to consider that the perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Given that the length of the rectangle is 25 cm twice its width, we can write the equation:
Length = 25cm + 2 * Width
Substituting this into the formula for the perimeter, we get:
Perimeter = 2(25cm + 2 * Width + Width)
Simplifying this equation, we have:
Perimeter = 2(25cm + 3 * Width)
Since the perimeter must be less than 335 cm, we can set up an inequality:
2(25cm + 3 * Width) < 335 cm
Now, let's solve this inequality to find the maximum dimensions.
First, divide both sides by 2 to eliminate the coefficient:
25cm + 3 * Width < 335 cm / 2
Simplifying, we have:
25cm + 3 * Width < 167.5 cm
Next, subtract 25cm from both sides:
3 * Width < 167.5 cm - 25cm
Simplifying further:
3 * Width < 142.5 cm
Finally, divide both sides by 3 to solve for Width:
Width < 142.5 cm / 3
Simplifying this:
Width < 47.5 cm
Since the dimensions must be integers, the maximum width of the table is 47 cm.
To find the maximum length, we can use the equation:
Length = 25cm + 2 * Width
Substituting the maximum value of Width, we have:
Length = 25cm + 2 * 47cm
Calculating, we find:
Length = 25cm + 94cm
Length = 119 cm
Therefore, the maximum dimensions of the table are 119 cm in length and 47 cm in width.