The length of a rectangle is 13 inches greater than its width,its perimeter is 8 feet.Find its dimension
L = W + 13
2L + 2W = 8*12 (converting to inches)
Substitute W+13 for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.
To find the dimensions of the rectangle, we need to use the given information about its length and width, as well as the information about its perimeter. Here's how we can proceed:
Let's assume the width of the rectangle is "x" inches.
According to the given information, the length of the rectangle is 13 inches greater than its width. Therefore, the length can be represented as "x + 13" inches.
We are also given that the perimeter of the rectangle is 8 feet. Since 1 foot is equal to 12 inches, we need to convert the perimeter from feet to inches:
Perimeter = 8 feet * 12 inches/foot = 96 inches.
The perimeter of a rectangle is given by the formula: Perimeter = 2 * (length + width).
Substituting the given values, we have: 96 = 2 * (x + 13 + x).
Simplifying the equation: 96 = 2 * (2x + 13).
Divide both sides of the equation by 2: 48 = 2x + 13.
Subtract 13 from both sides: 48 - 13 = 2x.
Simplifying, we get: 35 = 2x.
Divide both sides of the equation by 2: 35/2 = x.
Therefore, the width of the rectangle is x = 17.5 inches.
Now we can find the length of the rectangle by substituting the value of width back into our original equation:
Length = x + 13 = 17.5 + 13 = 30.5 inches.
So, the dimensions of the rectangle are:
Width = 17.5 inches
Length = 30.5 inches.