the length of rectangle is x cm .the width of the rectangle is 4cm less than the length.
A. write an expression in terms of x for the width of the rectangle
B. write the expression for the perimeter of the rectangle in terms of x
C. the perimeter of the rectangle is 20 cm.write an equation to find the value of x.
length ---- x
width = x-4, (it said so)
b) perimeter = all the way around = 2x + 2(x-4)
= ..... , simplify it
c) set your expression from b) equal to 20 and solve for x
A. To find the expression for the width of the rectangle, we know that the width is 4 cm less than the length. Therefore, we can express it as:
Width = Length - 4
B. The perimeter of a rectangle is defined as the sum of all its sides. In this case, the rectangle has two sides of length x and two sides of width (x - 4). Thus, the expression for the perimeter of the rectangle is:
Perimeter = 2(length) + 2(width)
Perimeter = 2x + 2(x - 4)
Perimeter = 2x + 2x - 8
Perimeter = 4x - 8
C. Since the perimeter of the rectangle is given as 20 cm, we can set up an equation to find the value of x:
Perimeter = 4x - 8
20 = 4x - 8
To solve the equation, we can isolate the variable on one side by adding 8 to both sides:
20 + 8 = 4x
28 = 4x
Finally, we divide both sides by 4 to solve for x:
28/4 = x
7 = x
Therefore, the value of x is 7 cm.