the perimeter of a rectangle is 226 inches. the length exceeds the width by 37 inches. find the length and the width.
P = 2L + 2W
226 = 2W + 2(W + 37)
226 = 4W + 74
226 - 74 = 4W
152 = 4W
38 = W
Take it from there.
To find the length and width of the rectangle, let's assign variables:
Let's say the width of the rectangle is x inches.
Since the length exceeds the width by 37 inches, the length would be x + 37 inches.
The perimeter of a rectangle is equal to the sum of all its sides. Hence, we can set up the following equation:
Perimeter = 2*(Length + Width)
Substituting the given values:
226 = 2*(x + 37 + x)
Let's simplify the equation:
226 = 2*(2x + 37)
226 = 4x + 74
To isolate the variable, let's subtract 74 from both sides:
226 - 74 = 4x
152 = 4x
Now, let's divide both sides by 4 to solve for x:
152/4 = x
38 = x
So, the width of the rectangle is 38 inches.
To find the length, we substitute the value of x in the equation for length:
Length = x + 37
Length = 38 + 37
Length = 75 inches
Therefore, the length of the rectangle is 75 inches and the width is 38 inches.