Analyzing Figures - SAT Subject Test in Math I
Card 0 of 5
The sides of a triangle have lengths 6 yards, 18 feet, and 216 inches. Which of the following is true about this triangle?
The sides of a triangle have lengths 6 yards, 18 feet, and 216 inches. Which of the following is true about this triangle?
One yard is equal to 3 feet; it is also equal to 36 inches. Therefore:
18 feet is equal to 
yards,
and
216 feet is equal to 
yards.
The three sides are congruent, making the triangle equilateral - and all equilateral triangles are acute.
One yard is equal to 3 feet; it is also equal to 36 inches. Therefore:
18 feet is equal to
and
216 feet is equal to
The three sides are congruent, making the triangle equilateral - and all equilateral triangles are acute.
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Figures not drawn to scale
The triangles above are similar. Given the measurements above, what is the length of side c?
Figures not drawn to scale
The triangles above are similar. Given the measurements above, what is the length of side c?
You can find the length of c by first finding the length of the hypotenuse of the larger similar triangle and then setting up a ratio to find the hypotenuse of the smaller similar triangle.
You also could have found 10 by recognizing this triangle is a form of a 3-4-5 triangle.
The hypotenuse of the bigger triangle is 10 inches.
Now that we know the length of the hypotenuse for the larger triangle, we can set up a ratio equation to find the hypotenuse of the smaller triangle.
cross multiply
You can find the length of c by first finding the length of the hypotenuse of the larger similar triangle and then setting up a ratio to find the hypotenuse of the smaller similar triangle.
You also could have found 10 by recognizing this triangle is a form of a 3-4-5 triangle.
The hypotenuse of the bigger triangle is 10 inches.
Now that we know the length of the hypotenuse for the larger triangle, we can set up a ratio equation to find the hypotenuse of the smaller triangle.
Compare your answer with the correct one above
If line 2 and line 3 eventually intersect when extended to the left which of the following could be true?
If line 2 and line 3 eventually intersect when extended to the left which of the following could be true?
Read the question carefully and notice that the image is deceptive: these lines are not parallel. So we cannot apply any of our rules about parallel lines. So we cannot infer II or III, those are only trueif the lines are parallel. If we sketch line 2 and line 3 meeting we will form a triangle and it is possible to make a = e. One such solution is to make a and e 60 degrees.
Read the question carefully and notice that the image is deceptive: these lines are not parallel. So we cannot apply any of our rules about parallel lines. So we cannot infer II or III, those are only trueif the lines are parallel. If we sketch line 2 and line 3 meeting we will form a triangle and it is possible to make a = e. One such solution is to make a and e 60 degrees.
Compare your answer with the correct one above
What is the maximum number of distinct regions that can be created with 4 intersecting circles on a plane?
What is the maximum number of distinct regions that can be created with 4 intersecting circles on a plane?
Try sketching it out.
Start with one circle and then keep adding circles like a venn diagram and start counting. A region is any portion of the figure that can be defined and has a boundary with another portion. Don't forget that the exterior (labeled 14) is a region that does not have exterior boundaries.
Try sketching it out.
Start with one circle and then keep adding circles like a venn diagram and start counting. A region is any portion of the figure that can be defined and has a boundary with another portion. Don't forget that the exterior (labeled 14) is a region that does not have exterior boundaries.
Compare your answer with the correct one above
Note: Figure may not be drawn to scale
In rectangle 
has length and width 
and 
respectively. Point 
lies on line segment 
and point 
lies on line segment 
. Triangle 
has area 
, in terms of 
and 
what is the possible range of values for 
?
Note: Figure may not be drawn to scale
In rectangle
Notice that the figure may not be to scale, and points 
and 
could lie anywhere on line segments and respectively.
Next, recall the formula for the area of a triangle:
To find the minimum area we need the smallest possible values for 
and 
.
To make 
smaller we can shift points 
and 
all the way to point 
. This will make triangle have a height of 
:
is the minimum possible value for the area.
To find the maximum value we need the largest possible values for 
and 
. If we shift point 
all the way to point 
then the base of the triangle is 
and the height is 
, which we can plug into the formula for the area of a triangle:
which is the maximum possible area of triangle
Notice that the figure may not be to scale, and points
Next, recall the formula for the area of a triangle:
To find the minimum area we need the smallest possible values for
To make
To find the maximum value we need the largest possible values for
which is the maximum possible area of triangle
Compare your answer with the correct one above