The length of a rectangle is 7cm greater than the width. Find the length and the width if the perimeter is 54cm
let x = width of rectangle
let x+7 = length o rectangle (since according to first statement, length is 7 greater than the width represented by x)
recall that perimeter of rectangle is:
P = 2*L + 2*W
substituting,,
54 = 2(x+7) + 2x
54 = 2x + 14 + 2x
54 = 4x + 14
54 - 14 = 4x
40 = 4x
40/4 = (4x)/4
x = 10 cm (width)
x+7 = 17 cm (length)
hope this helps~ :)
To solve this problem, we can use the information given and set up an equation based on the perimeter of the rectangle.
Let's denote the width of the rectangle as "w" cm. Since the length is 7 cm greater than the width, we can represent the length as "w + 7" cm.
The formula for the perimeter of a rectangle is P = 2(length + width).
According to the problem, the perimeter is given as 54 cm. So, we can substitute the values into the equation:
54 = 2(w + (w + 7))
Simplifying the equation:
54 = 2(2w + 7)
54 = 4w + 14
54 - 14 = 4w
40 = 4w
w = 10
The width of the rectangle is 10 cm.
To find the length, we substitute the value of the width back into the expression for the length:
Length = Width + 7 = 10 + 7 = 17 cm
Therefore, the length of the rectangle is 17 cm and the width is 10 cm.