A pentagon with a perimeter of one mile has three congruent sides. The second-longest side is 250 feet longer than any one of those three congruent sides, and the longest side is 500 feet longer than the second-longest side.

Which is the greater quantity?

(a) The length of the longest side of the pentagon

(b) Twice the length of one of the three shortest sides of the pentagon

One side of a regular pentagon is 20% longer than one side of a regular hexagon. Which is the greater quantity?

(A) The perimeter of the pentagon

(B) The perimeter of the hexagon

One side of a regular hexagon is 20% shorter than one side of a regular pentagon. Which is the greater quantity?

(A) The perimeter of the pentagon

(B) The perimeter of the hexagon

A rectangle has perimeter 140 inches and area 1,200 square inches. Which is the greater quantity?

(A) The length of a diagonal of the rectangle.

(B) 4 feet

One side of a regular pentagon is 20% longer than one side of a regular hexagon. Which is the greater quantity?

(A) The perimeter of the pentagon

(B) The perimeter of the hexagon

and are right triangles, with right angles , respectively.

Which is the greater quantity?

(a) The perimeter of

(b) The perimeter of

The lengths of the hypotenuses of ten similar right triangles form an arithmetic sequence. The smallest triangle has legs of lengths 5 and 12 inches; the second-smallest triangle has a hypotenuse of length one and one half feet.

Which of the following responses comes closest to the area of the largest triangle?

and are right triangles, with right angles , respectively. and .

Which is the greater quantity?

(a)

(b)

Given Trapezoid , where . Also,

Which is the greater quantity?

(a)

(b)

In Rhombus , and . Which is the greater quantity?

(A)

(B)