Other 2-Dimensional Geometry - SAT Subject Test in Math II
Card 0 of 6
The above figure shows a square garden (in green) surrounded by a dirt path six feet wide throughout. Which of the following expressions gives the distance, in feet, from one corner of the garden to the opposite corner?
The above figure shows a square garden (in green) surrounded by a dirt path six feet wide throughout. Which of the following expressions gives the distance, in feet, from one corner of the garden to the opposite corner?
The sidelength of the garden is 
less than that of the entire lot - that is, 
. Since the garden is square, the path from one corner to the other is a diagonal of a square, which has length 
times the sidelength. This is
feet.
The sidelength of the garden is
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Which of the following describes a triangle with sides of length 9 feet, 4 yards, and 180 inches?
Which of the following describes a triangle with sides of length 9 feet, 4 yards, and 180 inches?
3 feet make a yard, so 9 feet is equal to 3 yards. 36 inches make a yard, so 180 inches is equal to 
yards. That makes this a 3-4-5 triangle. 3-4-5 is a well-known Pythagorean triple; that is, they have the relationship
and any triangle with these three sidelengths is a right triangle. Also, since the three sides are of different lengths, the triangle is scalene.
The correct response is that the triangle is right and scalene.
3 feet make a yard, so 9 feet is equal to 3 yards. 36 inches make a yard, so 180 inches is equal to
and any triangle with these three sidelengths is a right triangle. Also, since the three sides are of different lengths, the triangle is scalene.
The correct response is that the triangle is right and scalene.
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Which of the following describes a triangle with sides of length two yards, eight feet, and ten feet?
Which of the following describes a triangle with sides of length two yards, eight feet, and ten feet?
Two yards is equal to six feet. The sidelengths are 6, 8, and 10, which form a well-known Pythagorean triple with the relationship
The triangle is therefore right. Since no two sides have the same length, it is also scalene.
Two yards is equal to six feet. The sidelengths are 6, 8, and 10, which form a well-known Pythagorean triple with the relationship
The triangle is therefore right. Since no two sides have the same length, it is also scalene.
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The above figure shows a square garden (in green) surrounded by a dirt path 
feet wide throughout. Which of the following expressions gives the distance, in feet, from one corner of the garden to the opposite corner?
The above figure shows a square garden (in green) surrounded by a dirt path
The sidelength of the garden is 
feet less than that of the entire lot - that is, 
. Since the garden is square, the path from one corner to the other is a diagonal of a square, which has length times the sidelength. This is
feet.
The sidelength of the garden is
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Figure is not drawn to scale
is a diameter of the circle; its length is ten; furthermore we know the following:
Give the length of 
(nearest tenth)
Figure is not drawn to scale
Give the length of
Locate 
, the center of the circle, which is the midpoint of 
; draw radius 
. 
is formed. The central angle that intercepts 
is 
, so 
. 
and 
, being radii of the circle, have length half the diameter of ten, or five. The diagram is below.
By the Law of Cosines, given two sides of a triangle of length 
and 
, and their included angle of measure 
, the length of the third side 
can be calculated using the formula
Setting 
, solve for 
:
Taking the square root of both sides:
Locate
By the Law of Cosines, given two sides of a triangle of length
Setting
Taking the square root of both sides:
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A circle is inscribed inside a square that touches all edges of the square. The square has a length of 3. What is the area of the region inside the square and outside the edge of the circle?
A circle is inscribed inside a square that touches all edges of the square. The square has a length of 3. What is the area of the region inside the square and outside the edge of the circle?
Solve for the area of the square.
Solve for the area of the circle. Given the information that the circle touches all sides of the square, the diameter is equal to the side length of the square.
This means that the radius is half the length of the square: 
Substitute the radius.
Subtract the area of the square and the circle to determine the area desired.
The answer is: 
Solve for the area of the square.
Solve for the area of the circle. Given the information that the circle touches all sides of the square, the diameter is equal to the side length of the square.
This means that the radius is half the length of the square:
Substitute the radius.
Subtract the area of the square and the circle to determine the area desired.
The answer is:
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