The length of a rectangle is 5 in longer than it's width. If the perimeter of the rectangle is 50 in find it's area
P = 2L + 2W
50 = 2(W + 5) + 2W
50 = 4W + 10
40 = 4W
10 = W
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A = LW
To find the area of a rectangle, we need to know its length and width. In this case, we are given some information about the rectangle's length and the perimeter. We can use this information to find the dimensions and then calculate the area.
Let's start by assigning variables to the width and length of the rectangle. Let's say the width is 'w' inches. The problem tells us that the length is 5 inches longer than the width, so the length would be 'w + 5' inches.
The perimeter of a rectangle is calculated by adding up all its sides. In this case, the perimeter is given as 50 inches. Since a rectangle has two pairs of equal sides (opposite sides are equal), we can set up the equation:
Perimeter = 2 * (length + width)
Substituting the values we assigned to width and length, we have:
50 = 2 * (w + (w + 5))
Now we can solve this equation to find the value of 'w', which represents the width.
50 = 2 * (2w + 5)
50 = 4w + 10
40 = 4w
w = 10
So the width of the rectangle is 10 inches. To find the length, we can substitute this value into our expression for the length: w + 5 = 10 + 5 = 15 inches.
Now that we know the width and length of the rectangle (10 inches and 15 inches respectively), we can find its area. The formula for the area of a rectangle is:
Area = length * width
Area = 10 inches * 15 inches = 150 square inches.
Therefore, the area of the rectangle is 150 square inches.