if area blue is 100cm^2 and area green is 576cm^2. What is the red area? Use the Pythagorean theorem method
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assume that the red area forms a right-angled triangle with sides "a" and "b", where "a" is adjacent to the blue area and "b" is adjacent to the green area. The hypotenuse, which represents the red area, will be the longest side and will have a length "c".
According to the theorem, we have the following relationship:
c^2 = a^2 + b^2
Now, we need to find the values of "a" and "b". We are given that the area of the blue region is 100cm^2, so:
a^2 = 100
Taking the square root of both sides, we get:
a = √100 = 10 cm
Similarly, the area of the green region is 576cm^2, so:
b^2 = 576
Taking the square root of both sides, we get:
b = √576 = 24 cm
Now, substituting these values into the Pythagorean theorem equation, we have:
c^2 = 10^2 + 24^2
c^2 = 100 + 576
c^2 = 676
Taking the square root of both sides, we find:
c = √676 = 26 cm
Thus, the red area has an area of:
Area = a * b / 2
Area = 10 * 24 / 2
Area = 120 cm^2
if area green is 400cm^2 but the area as a whole is 641cm^2. What is the missing leg? Use the Pythagorean theorem method
Let's assume that the missing leg of the right triangle is "a" and the known leg is "b". The hypotenuse, which represents the missing leg, will be "c".
According to the Pythagorean theorem, we have the relation:
c^2 = a^2 + b^2
We are given that the area of the green region is 400 cm^2. Since the area of a rectangle is equal to the product of its two sides, we can find the length of the known leg:
b^2 = 400
Taking the square root of both sides, we get:
b = √400 = 20 cm
Now, let's find the missing leg "a". We are also given that the total area of the rectangle is 641 cm^2, which is the sum of the areas of the green region and the missing leg.
Therefore, we have the equation:
641 = 400 + a^2
Rearranging this equation, we get:
a^2 = 641 - 400
a^2 = 241
Taking the square root of both sides, we find:
a = √241 ≈ 15.524 cm
Thus, the missing leg has a length of approximately 15.524 cm.
if area green is 400cm^2 but the area as a whole is 841cm^2. What is the missing leg? Use the Pythagorean theorem method
Let's assume that the missing leg of the right triangle is "a" and the known leg is "b". The hypotenuse, which represents the missing leg, will be "c".
According to the Pythagorean theorem, we have the relation:
c^2 = a^2 + b^2
We are given that the area of the green region is 400 cm^2. Since the area of a rectangle is equal to the product of its two sides, we can find the length of the known leg:
b^2 = 400
Taking the square root of both sides, we get:
b = √400 = 20 cm
Now, let's find the missing leg "a". We are also given that the total area of the rectangle is 841 cm^2, which is the sum of the areas of the green region and the missing leg.
Therefore, we have the equation:
841 = 400 + a^2
Rearranging this equation, we get:
a^2 = 841 - 400
a^2 = 441
Taking the square root of both sides, we find:
a = √441 = 21 cm
Thus, the missing leg has a length of 21 cm.
if area blue is 9cm^2 and area green is 12cm^2. What is the red area? Use the Pythagorean theorem method
Let's assume that the red area forms a right-angled triangle with sides "a" and "b", where "a" is adjacent to the blue area and "b" is adjacent to the green area. The hypotenuse, which represents the red area, will be the longest side and will have a length "c".
According to the Pythagorean theorem, we have the following relationship:
c^2 = a^2 + b^2
We are given that the area of the blue region is 9 cm^2, so we can find the length of "a":
a^2 = 9
Taking the square root of both sides, we get:
a = √9 = 3 cm
Similarly, the area of the green region is 12 cm^2, so we can find the length of "b":
b^2 = 12
Taking the square root of both sides, we get:
b = √12
Now, substituting these values into the Pythagorean theorem equation, we have:
c^2 = 3^2 + (√12)^2
c^2 = 9 + 12
c^2 = 21
Taking the square root of both sides, we find:
c = √21 ≈ 4.583 cm
Thus, the red area has an area of:
Area = a * b / 2
Area = 3 * (√12) / 2
Area ≈ 5.196 cm^2
if area blue is 9cm and area green is 12cm. What is the red area? Use the Pythagorean theorem method
Based on the information provided, we can assume that the blue and green areas form a right-angled triangle. Let's assume that the blue area is the base (b) and the green area is the height (h) of the triangle.
The area of a triangle can be calculated using the formula: Area = (base * height) / 2
Given that the blue area is 9 cm and the green area is 12 cm, we can set up the following equation:
(9 * 12) / 2 = (b * h) / 2
Simplifying this equation, we get:
108 = b * h
Now, we need to find the missing side, which represents the red area (a).
Using the Pythagorean theorem, we have the relation:
a^2 = b^2 + h^2
We know that b = 9 and h = 12, so we can substitute these values into the Pythagorean theorem equation:
a^2 = 9^2 + 12^2
a^2 = 81 + 144
a^2 = 225
Taking the square root of both sides, we find:
a = √225 = 15 cm
Thus, the red area has an area of 15 cm.
if area green is 16cm^2 but the area as a whole is 34cm^2. What is the missing leg? Use the Pythagorean theorem method
Let's assume that the missing leg of the right triangle is "a" and the known leg is "b". The hypotenuse, which represents the missing leg, will be "c".
According to the Pythagorean theorem, we have the relation:
c^2 = a^2 + b^2
We are given that the area of the green region is 16 cm^2. Since the area of a rectangle is equal to the product of its two sides, we can find the length of the known leg:
b^2 = 16
Taking the square root of both sides, we get:
b = √16 = 4 cm
Now, let's find the missing leg "a". We are also given that the total area of the rectangle is 34 cm^2, which is the sum of the areas of the green region and the missing leg.
Therefore, we have the equation:
34 = 16 + a^2
Rearranging this equation, we get:
a^2 = 34 - 16
a^2 = 18
Taking the square root of both sides, we find:
a = √18 ≈ 4.243 cm
Thus, the missing leg has a length of approximately 4.243 cm.