The perimeter of a rectangle is 90 units the base is 3z and the side is 4z+3 what is the length
2(3z) + 2(4z+3) = 90
Solve for z, then 3z or 4z+3, whichever one is the length. (I assume it is the base.)
To find the length of a rectangle given its perimeter and base, you can use the formula for the perimeter of a rectangle, which is:
Perimeter = 2(base) + 2(side)
Given that the perimeter is 90 units and the base is 3z, and the side is 4z + 3, we can substitute these values into the formula:
90 = 2(3z) + 2(4z + 3)
Simplifying:
90 = 6z + 8z + 6
Combining like terms:
90 = 14z + 6
Subtracting 6 from both sides:
90 - 6 = 14z
84 = 14z
Dividing both sides by 14:
84/14 = z
6 = z
So the value of z is 6.
Now, we can find the length by substituting the value of z into either the base or the side. Let's use the side, which is 4z + 3:
Length = 4z + 3
= 4(6) + 3
= 24 + 3
= 27
Therefore, the length of the rectangle is 27 units.
To find the length of the rectangle, we need to use the formula for the perimeter of a rectangle, which is the sum of all four sides. In this case, the perimeter is given as 90 units.
Let's break down the information given:
The base of the rectangle is 3z.
The side of the rectangle is 4z + 3.
According to the formula for the perimeter, we can write the equation:
2 * (base + side) = perimeter
Replacing the base and side with the given values:
2 * (3z + 4z + 3) = 90
Simplifying the equation:
2 * (7z + 3) = 90
14z + 6 = 90
Subtracting 6 from both sides of the equation:
14z = 84
Dividing both sides of the equation by 14:
z = 6
Now, we can find the length of the rectangle by substituting the value of z back into the side equation:
Length = 4z + 3
Length = 4(6) + 3
Length = 24 + 3
Length = 27 units.
Therefore, the length of the rectangle is 27 units.