The large rectangle shown, is composed of five congruent smaller rectangles, each with whole number dimensions. If the perimeter of each smaller rectangle is 20 com, find the are of the entire large rectangle in sq cm.
I don't see the diagram, so I can think of many possible answers, all the way from 45 to 125.
Let's assume the length of one of the smaller rectangles is x cm and the width is y cm.
We know that the perimeter of each smaller rectangle is 20 cm, so we can write two equations:
2x + 2y = 20 (Equation 1)
Since the large rectangle is composed of five congruent smaller rectangles, the length of the large rectangle will be 5 times the length of the smaller rectangle, and the width of the large rectangle will be the same as the width of the smaller rectangle. Therefore, we can write:
Length of large rectangle = 5x
Width of large rectangle = y
The area of the large rectangle can be calculated by multiplying the length and width:
Area of large rectangle = (5x) * y = 5xy
Now, we need to solve Equation 1 to find the values of x and y.
From Equation 1, we have:
2x + 2y = 20
Dividing both sides by 2, we get:
x + y = 10 (Equation 2)
Now, we have a system of equations:
x + y = 10 (Equation 2)
5xy = Area of large rectangle
Since we don't have specific values for x and y, we can't determine the exact area of the large rectangle. However, we can provide a general formula to calculate the area based on x and y.
So, the area of the entire large rectangle in square centimeters is 5xy.
To find the area of the entire large rectangle, we first need to determine the dimensions of the smaller rectangles.
Let's assume the length of one small rectangle is L and the width is W.
The perimeter of each smaller rectangle is given as 20 cm. The formula for the perimeter of a rectangle is 2 * (length + width), so we can write the equation as:
2 * (L + W) = 20
Now, we know that the large rectangle is composed of five congruent smaller rectangles. Therefore, the length of the large rectangle is 5L, and the width is W.
To find the area of the entire large rectangle, we multiply its length by its width:
Area = Length * Width = (5L)(W)
Now, we need to solve for L and W in order to calculate the area.
From the equation 2 * (L + W) = 20, we can simplify it to L + W = 10.
Since L and W are whole numbers, let's consider the possible values for L and W that satisfy the equation L + W = 10:
L = 1, W = 9
L = 2, W = 8
L = 3, W = 7
L = 4, W = 6
L = 5, W = 5
Next, we need to check which of these pairs of values for L and W satisfy the condition that the perimeter of each smaller rectangle is 20 cm.
By substituting the values, we can verify that only L = 4 and W = 6 satisfy 2 * (L + W) = 20.
Now, we can calculate the area of the entire large rectangle:
Area = (5L)(W) = (5 * 4)(6) = 20 * 6 = 120 sq cm
Therefore, the area of the entire large rectangle is 120 square centimeters.