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The lengths of two legs of a right triangle are 1 and x, respectively, while the length of the hypotenuse of the right triangle is y.

Quantity A: y

Quantity B: 1+$$x^{2}$$


The figure shows two congruent circles with centers $$P$$ and $$Q$$. If $$RP=QS=1$$ and $$XY=8$$, what is the distance between centers $$P$$ and $$Q$$?
Two line segments of equal length bisect each other.

Quantity A

The number of circles that pass through at least three of the four endpoints

Quantity B

2




The figure shows part of the frame of an office building under construction, where points P, Q, and R are located on the frame at different heights and Q is 8.4 meters directly above P. The line of vision through Q and R makes an angle of 30 degrees with the upper horizontal floor, represented by line segment QS, and the line of vision through P and R makes an angle of 60 degrees with the lower horizontal floor, represented by line segment PT. What is the height of R, in meters, above the lower floor?


EF is parallel to the side of the rectangle ABCD

Quantity A:The area of the shaded region

Quantity B:18


Square BDFG is inscribed in isosceles triangle ACE. If the area of triangular region ACE is 1, what is the area of triangular region BCD?


The figure above represents six straight city streets that will be repaved. The figure shows only the centerlines of the streets, and all the streets have the same width. Four of the streets are parallel, with centerlines that are 200 meters apart from each other. If the cost to repair each street is estimated as $72,000 per kilometer of the length of its centerline, what is the total estimated cost to repave the six streets?

$_____


The area of square region ABIH equals the area of square region JDEF. Quadrilateral BJFI is a parallelogram. The area of squared region ACEG is 9 times the area of square region ABIH.

Quantity A

The area of ABIH

Quantity B

The area of BJFI




Square ABCD and parallelogram AEFD lie in the same plane, and AB=AE.

Quantity A

The area of region ABCD

Quantity B

The area of region AEFD


Parallelogram ABCD has adjacent sides of length 10 and 16.

Quantity A

The area of the region enclosed by ABCD

Quantity B

155


The perimeter of parallelogram ABCD is 360 feet.

Quantity A:The length of diagonal AC

Quantity B:90 $$\sqrt{2}$$ feet
In the xy-plane, if three of the vertices of a parallelogram have coordinates (2, -1), (1, 2), and (5, 1), which of the following could be the coordinates of the fourth vertex?

Indicate all such coordinates
The lengths of two diagonals of a parallelogram are 10 and 24, respectively. If the two diagonals are perpendicular to each other, then what is the perimeter of the parallelogram?


ABCD is a square, AEFG is a rectangle, and BE=DG.

Quantity A

The area of square ABCD

Quantity B

The area of rectangle AEFG


The width of rectangle A is 9, and its area is 90.

The length of rectangle B is 12, and its area is 120.

Quantity A

The length of rectangle A

Quantity B

The width of rectangle B


Square A is bigger than square B

The ratio of two squares` diagonal is 2:1

Quantity A

The ratio of two squares` area (A to B)

Quantity B

4




The figure represents a flat rectangular plot of land that consists of a rectangular parking lot and a surrounding sidewalk of uniform width. If the area of the parking lot is $$\frac{3}{5}$$ of the area of the entire plot of land, what is the width, in feet, of the sidewalk?


ABCD is a square, and the shaded regions are square.

Quantity A

The area of the shaded region / the area of unshaded region

Quantity B

$$\frac{x}{y}$$




Which line(s), k, l or n, can divide the rectangle into two parts that have an area ratio of 2:1?

Indicate all such lines.
Each side of square S has length 2. Five different points lie inside S but not on the sides of S.

Quantity A

The distance between the closest two points among the five points

Quantity B

$$\sqrt{2}$$


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