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20.07.2021 •
Mathematics
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
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Ответ:
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..."
Ответ:
therefore sin x = opposite / hypotenuse
sin x = 4 / 5
sin x = 0.8
x = sin^(-1) 0.8
x = 53.13°
answer: the measure of angle x is 53.13°.