the greastest area that a rectangle whose perimeter is 52m cm have is
It must be a square, find the sides, then the area
is myy procedure correct
first i made a square 52/4=13
than i try changing the square to a rectangle by multiplying 16x13 but the answer was 208
than i did 14x12 which is 168 and that was one of the choices
A square of sides 13 has a perimeter of 52 and its area will be 13 x 13 or 169, which is larger than 168.
I sure hope 169 is one of your choices or else they are wrong.
BTW a square is a rectangle.
To find the greatest area of a rectangle with a given perimeter, we need to determine the dimensions that will maximize the area. In this case, the perimeter is given as 52 cm.
Let's denote the length of the rectangle as L and the width as W.
To maximize the area, we can use the fact that the perimeter of a rectangle is given by the formula: 2L + 2W = Perimeter.
Substituting the given perimeter of 52 cm into the equation, we have: 2L + 2W = 52 cm.
Simplifying this equation, we can divide both sides by 2: L + W = 26 cm.
To maximize the area, we need to understand that the area of a rectangle is given by the formula: A = L * W.
Now we have two approaches to find the greatest area:
1. Solve the equation L + W = 26 for one of the variables (either L or W) and substitute it back into the area formula, then find the derivative of the area function, set it to zero, and solve for the other variable. However, this involves calculus and is more complex.
2. Implement a trial and error method to find the dimensions that maximize the area. We know that the sum of the length and width must be 26 cm, so let's start by testing some possible pairs of L and W to see which combination yields the greatest area while satisfying the given conditions.
Here are a few examples:
- L = 13 cm, W = 13 cm (giving a total of 26 cm)
- L = 14 cm, W = 12 cm (giving a total of 26 cm)
- L = 15 cm, W = 11 cm (giving a total of 26 cm)
- And so on...
By calculating the area for each of these combinations, we can compare the results to find the greatest area.
For example, by using L = 13 cm and W = 13 cm, the area would be A = L * W = 13 cm * 13 cm = 169 cm^2.
By repeating this process for each combination, you will eventually find the dimensions that produce the greatest area.