perimeter of a rectangle is 10
times the width. The length is 9
metres more than the width.Find the width of the rectangle.
P = 10W
L = W+9
2L + 2W = P
2(W+9) + 2W = 10W
Solve for W.
I have this same question in my maths textbook and the answer says 3 meters and I don't understand how they got that answer
To find the width of the rectangle, we need to set up an equation with the given information. Let's denote the width of the rectangle as 'w'.
Given that the perimeter of the rectangle is 10 times the width, we can write the equation as:
2 × (length + width) = 10 × width
Since the length is given as 9 meters more than the width, we can express the length as:
length = width + 9
Substituting this value into the equation for the perimeter, we get:
2 × (width + (width + 9)) = 10 × width
Simplifying the expression, we have:
2 × (2 × width + 9) = 10 × width
Expanding the brackets, we get:
4 × width + 18 = 10 × width
Subtracting 4w from both sides, we obtain:
18 = 6 × width
Dividing both sides by 6, we find:
width = 3
Therefore, the width of the rectangle is 3 meters.