a rectangle is 13 cm longer than it is wide. its perimeter is 226 cm. find its length and width.
To find the length and width of the rectangle, we can set up a system of equations using the information given.
Let's say the width of the rectangle is "w" cm.
It is given that the rectangle is 13 cm longer than it is wide. So, the length can be represented as "w + 13" cm.
The perimeter of a rectangle is calculated by adding up the lengths of all its sides. For a rectangle, the perimeter is calculated by using the formula: P = 2w + 2l, where P is the perimeter, w is the width and l is the length.
Given that the perimeter of the rectangle is 226 cm, we can set up the following equation:
226 = 2w + 2(w + 13)
Solving this equation will give us the value of the width.
226 = 2w + 2w + 26
226 = 4w + 26
4w = 200
w = 50
So, the width of the rectangle is 50 cm.
Now, to find the length, we substitute the value of the width (w = 50) into the expression for the length:
Length = width + 13 = 50 + 13 = 63 cm
Therefore, the length of the rectangle is 63 cm and the width is 50 cm.