Geometry

If p is the perimeter of rectangle Q, what is the value of p? (1) Each diagonal of rectangle Q has length 10. (2) The area of rectangle Q is 48.

What is the perimeter of isosceles triangle MNP? (1) MN = 16 (2) NP = 20

Can a certain rectangular sheet of glass be positioned on a rectangular tabletop so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop? (1) The tabletop is 36 inches wide by 60 inches long. (2) The area of one side of the sheet of glass is 2,400 square inches.

In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangular region RCS ? (1) The area of triangular region ABX is 32. (2) The length of one of the altitudes of triangle ABC is 8.

If arc PQR above is a semicircle, what is the length of diameter PR ? (1) a = 4 (2) b = 1

In the figure above, what is the value of x + y ? (1) x = 70 (2) ABC and ADC are both isosceles triangles

In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ? (1) The coordinates of point P are (6,8) (2) The coordinates of point Q are (13,0)

If the area of triangular region RST is 25, what is the perimeter of RST? (1) The length of one side of RST is 5 2 √ 5 2 . (2) RST is a right isosceles triangle.

In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS? (1) Triangle QTR is equilateral. (2) Segments PT and TS have equal length.

A rectangle is defined to be "silver" if and only if the ratio of its length to its width is 2 to 1. If rectangle S is silver, is rectangle R silver? (1) R has the same area as S (2) The ratio of one side of R to one side of S is 2 to 1.

In ΔPQR above is PQ > RP? (1) x = y (2) y = z

In the figure above, R and Q are points on the x-axis. What is the area of equilateral triangle PQR ? (1) The coordinates of point Pare (6, 2 3 √ 2 3 ) . (2) The coordinates of point Q are (8, 0).

In parallelogram ABCD , what is the measure of ∠ADC? (1) The measure of ∠ABC is greater than 90 (2) The measure of ∠BCD is 70

What is the maximum number of rectangular blocks, each with dimensions 12 centimeters by 6 centimeters by 4 centimeters, that will fit inside rectangular box X? (1) When box X is filled with the blocks and rests on a certain side, there are 25 blocks in the bottom layer. (2) The inside dimensions of box X are 60 centimeters by 30 centimeters by 20 centimeters.

In the figure above, what is the ratio KN/MN? (1) The perimeter of rectangle KLMN is 30 meters. (2) The three small rectangles have the same dimensions.

Is the triangle above equilateral? (1) x = y (2) z = 60

The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and B, as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A? (1) The base has area 250 square feet. (2) The center of the base is 20 feet from point C.

In triangle XYZ, whatis the length of YZ? (1) The length of XY is 3. (2) The length of XZ is 5.

An empty rectangular swimming pool has uniform depth. How long will it take to fill the pool with water? (1) Water will be pumped in at the rate of 240 gallons per hour (1 cubic foot = 7.5 gallons) (2) The pool is 60 feet long and 25 feet wide

The perimeter of a rectangular garden is 360 feet. What is the length of the garden? (1) The length of the garden is twice the width. (2) The difference between the length and width of the garden is 60 feet.