10. A rectangle whose length is twice its width has a diagonal equal to one side of a given square. The ratio of the area of the rectangle to the area of the square is​

2/5

Step-by-step explanation:

First, we can draw the rectangle out, as shown. The length is twice the width, and the diagonal, y, cuts across the rectangle. This forms a right triangle, and using the Pythagorean Theorem, we can say that

y² = x² + (2x)²

y² = x² + 4x²

y² = 5x²

square root both sides

y=√(5x²)

The diagonal, or y, is equal to √(5x²). This is equal to one side of the square

The area for the rectangle, which we need to find for the ratio, is length * width = x * 2x = 2x²

The area for the square, which we also need to find for the ratio, is (side length)² = √(5x²) = 5x²

The ratio for the area of the rectangle to the area of the square is therefore 2x²/5x² = 2/5 (crossing out the x² in both the numerator and the denominator). We know to put the rectangle on top because of the specific wording of "the ratio of the area of the rectangle to..."

the answer will be the last one

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation: