the length of a rectangle is 3cm more than twice the width. the perimeter is 84cm. find the length
length= 29cm
To find the length of the rectangle, we can set up an equation using the given information.
Let's assume the width of the rectangle is represented by 'w' cm.
According to the problem, the length of the rectangle is 3 cm more than twice the width. This can be expressed as:
Length = 2w + 3
The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, we know the perimeter is 84 cm.
Perimeter = 2(Length + Width)
Substituting the given values, we get:
84 = 2((2w + 3) + w)
Now we can solve this equation to find the value of 'w', which represents the width:
84 = 2(3w + 3)
Divide both sides of the equation by 2:
42 = 3w + 3
Subtract 3 from both sides:
39 = 3w
Divide both sides by 3:
w = 13
So the width of the rectangle is 13 cm.
Now, substitute this value back into the expression for the length:
Length = 2w + 3
Length = 2(13) + 3
Length = 26 + 3
Length = 29
Therefore, the length of the rectangle is 29 cm.