the perimeter of a rectangle is 62 m. then length is 10 m more than twice the width. find the dimensions
what is the length?
what is the width?
2L + 2W = P
L = 10 + 2W
2(10 + 2W) + 2W = 62
20 + 4W + 2W = 62
6W = 42
W = 7
L = 14 + 10
L = 24
Check my figures.
To find the dimensions of the rectangle, we can use the given information about the perimeter and the relationship between the length and the width.
Let's assume that the width of the rectangle is 'w'. According to the problem, the length is 10 meters more than twice the width, so the length can be represented as '2w + 10'.
Now, we know that the perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
In this case, the perimeter is given as 62 meters. Substituting the length and width values into the formula, we get:
62 = 2(2w + 10 + w)
Simplifying this equation, we have:
62 = 2(3w + 10)
Dividing both sides of the equation by 2, we get:
31 = 3w + 10
Subtracting 10 from both sides, we have:
21 = 3w
Finally, dividing both sides by 3, we find:
w = 7
So, the width of the rectangle is 7 meters.
To find the length, we can substitute the value of 'w' back into our length equation:
Length = 2w + 10
Length = 2(7) + 10
Length = 14 + 10
Length = 24
Therefore, the length of the rectangle is 24 meters.
In conclusion, the dimensions of the rectangle are:
Width = 7 meters
Length = 24 meters