A rectangle has one side of 3 feet and a diagonal of 3.28 ft. What is the area of the rectangle? No Pythagorean Theorem.
Why no Pythagorean Theorem? It would do the job to give the other side's length. Then you could just multiply the two sides.
To find the area of the rectangle, we need to know the length of the other side. Since the question mentions that the diagonal of the rectangle is 3.28 ft, we can use this information to find the length of the missing side without using the Pythagorean theorem.
Let's denote the length of the missing side as x. We know that the diagonal of the rectangle divides it into two right triangles. The sides of these triangles are the length of the missing side x, the given side of 3 ft, and the diagonal of 3.28 ft.
Using the Pythagorean theorem, we can write the equation:
x^2 + 3^2 = 3.28^2
Simplifying this equation, we have:
x^2 + 9 = 10.7584
Subtracting 9 from both sides, we get:
x^2 = 1.7584
To solve for x, we take the square root of both sides:
x = √1.7584
Using a calculator, we find that x is approximately 1.325 ft.
Now that we know the lengths of both sides of the rectangle (3 ft and 1.325 ft), we can calculate its area by multiplying these sides:
Area = length × width = 3 ft × 1.325 ft ≈ 3.975 square feet.
Therefore, the area of the rectangle is approximately 3.975 square feet.