the perimeter of a rectangle is 72. the base is 3 times the height find the area of the rectangle
2(3h+h) = 72
8h = 72
...
To find the area of a rectangle, we need both the length (base) and the width (height) of the rectangle. In this case, we are given that the perimeter of the rectangle is 72, and the base is 3 times the height.
Let's assume the height of the rectangle is H.
According to the given information, the base of the rectangle is 3 times the height, so the base would be 3H.
Now, let's calculate the perimeter of the rectangle:
The perimeter of a rectangle is given by the formula: P = 2(L + W),
where P represents the perimeter, L represents the length (base), and W represents the width (height).
Here, the perimeter is given as 72, so we can write the equation as:
72 = 2(3H + H)
Simplifying the equation:
72 = 2(4H)
72 = 8H
Divide both sides of the equation by 8:
H = 9
Now, substitute H back into the equation to find the base (L):
L = 3H = 3(9) = 27
So, the dimensions of the rectangle are:
Base (length) = 27
Height (width) = 9
Finally, to find the area of the rectangle, we use the formula: A = L × W:
A = 27 × 9 = 243
Therefore, the area of the rectangle is 243 square units.