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For the convex polygon above, which of the following intervals contains all possible value of x?

In a quadrilateral ABCD, AB=4, AD=7, BC=5, then the range of CD is?
What is the probability of forming a triangle when randomly selecting three numbers as three sides out of 4, 5, 7, 8, 11?
Give your answer as a fraction.
If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the area?
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24

Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC above?
Indicate all such statements.
In an isosceles triangle, the length of one of the three sides is 5, while the total length of two sides is 10.

Quantity A

The perimeter of the triangle

Quantity B

15


In an isosceles triangle △ABC, ∠A=62°

Quantity A

∠B

Quantity B

∠C



Quantity A

The perimeter of rectangular

Quantity B

The sum of the perimeter of two triangles



Quantity A

$$\frac{BD}{AB}$$

Quantity B

$$\frac{DC}{BC}$$



Quantity A

The area of triangle PQR

Quantity B

The area of triangle PSR


The ratio of the length of three sides of a triangle is 3:5:7

Quantity A

The degree of the largest angle in the triangle

Quantity B

84°



Quantity A: The length of IJ
Quantity B: 5


AB∥ED,△ABC and EDC are similar triangles, and the area of △EDC equals to $$\frac{1}{9}$$ of the area of △ABC. What is the ratio of EC to AE?

Give your asnwer as a fraction.
In the xy-plane, one of the vertices of square S is the point (2, 2). The diagonals of S intersect at the point (6, 6).

Quantity A

The area of S

Quantity B

64



The figure above represents a rectangular garden with a walkway around it. The garden is 18 feet long and 12 feet wide. The walkway is uniformly 3 feet wide, and its edges meet at right angles. What is the area of the walkway?
A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on the fourth side. If the entire length of the fence is 140 feet, then which of the following could be the length, in feet, of one of the sides of the flower bed?
Indicate all such lengths.
The number of points of intersection between an equilateral triangle and a square could be (such that none of the sides would be overlapping)?
Indicate all that is/are true.

Quantity A

Area of a rectangle with perimeter 20

Quantity B

Area of a triangle with base 5 and height 10


Set A consists of 40 integers, and set B consists of 150 integers. The number of integers that are in both set A and set B is 20.

Quantity A

The total number of integers that are in set A or set B, or both

Quantity B

170


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