The width of a rectangle is 6 feet, and the diagonal is 10 feet. What is the area of the rectangle?
Use the Pythagorean theorem (a^2 + b^2 = c^2), where c = hypotenuse.
6^2 + x^2 = 10^2
Once you find x, multiply by 6 to get area.
Check out your answers for the second post using the same theorem.
To find the area of a rectangle, we need to know the length and width. In this case, we have the width, which is 6 feet. However, we do not have the length. We are given the diagonal, but we cannot directly use it to calculate the length.
To find the length of the rectangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides (the length and width). In this case, we can create a right-angled triangle using the length, width, and diagonal as the hypotenuse.
Let's assign the length of the rectangle as "L". According to the Pythagorean theorem, we have:
L^2 + 6^2 = 10^2
Simplifying the equation, we get:
L^2 + 36 = 100
Subtracting 36 from both sides, we get:
L^2 = 64
Taking the square root of both sides, we find:
L = 8
Now that we know the length of the rectangle (L = 8) and the width (6), we can calculate the area of the rectangle by multiplying the length and width:
Area = Length × Width
= 8 × 6
= 48 square feet
Therefore, the area of the rectangle is 48 square feet.
Which of the following are measurements of the sides of a right triangle?
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A. 3, 4, 5
B. 28, 26, 12
C. 17, 14, 6
D. all of the above