All SSAT Upper Level Math Resources
Example Questions
Example Question #1 :Perimeter Of A Triangle
What is the perimeter of a right triangle with hypotenuseand a leg of length?
It cannot be determined from the information given.
Using the Pythagorean Theorem, the length of the second leg can be determined.
We are given the length of the hypotenuse and one leg.
The perimeter of the triangle is the sum of the lengths of the sides.
Example Question #1 :Right Triangles
Which of these polygons has the same perimeter as a right triangle with legs 6 feet and 8 feet?
A regular pentagon with sidelength one yard.
定期与sidelength八角一个院子。
A regular decagon with sidelength one yard.
A regular hexagon with sidelength one yard.
None of the other responses is correct.
定期与sidelength八角一个院子。
A right triangle with legs 6 feet and 8 feet has hypotentuse 10 feet, as this is a right triangle that confirms to the well-known Pythagorean triple 6-8-10. The perimeter is thereforefeet, or 8 yards.
We are looking for a polygon with this perimeter. Each choice is a polygon with all sides one yard long, so we want the polygon with eight sides - the regular octagon is the correct choice.
Example Question #1 :How To Find The Perimeter Of A Right Triangle
The lengths of the legs of a right triangle areunits andunits. What is the perimeter of this right triangle?
units
units
units
units
units
First, we need to use the Pythagorean Theorem to find the hypotenuse of the triangle.
Now, add up all three side lengths to find the perimeter of the triangle.
Example Question #2 :Right Triangles
A right triangle has leg lengths ofand. Find the perimeter of this triangle.
First, use the Pythagorean Theorem to find the length of the hypotenuse.
Substituting inandforand(the lengths of the triangle's legs), we get:
Now, add up the three sides to find the perimeter:
Example Question #3 :Right Triangles
What is the perimeter of a right triangle with legs of lengthand, respectively?
In order to find the perimeterof the right triangle, we need to first find the missing length of the hypotenuse. In order to find the hypotenuse, use the Pythagorean Theorem:
, whereandare the lengths of the legs of the triangle, andis the length of the hypotenuse.
Substituting in our known values:
Now that we have the lengths of all sides of the right triangle, we can calculate the perimeter:
Example Question #4 :Right Triangles
What is the perimeter of a right triangle with a hypotenuse of lengthand a leg of length?
Not enough information provided
In order to find the perimeterof the right triangle, we need to first find the missing length of the second leg. In order to find the second leg, use the Pythagorean Theorem:
, whereandare the lengths of the legs of the triangle, andis the length of the hypotenuse.
Substituting in our known values:
Subtractingfrom each side of the equation lets us isolate the variable for which we are solving:
Now that we have the lengths of all three sides of the right triangle, we can calculate the perimeter:
Example Question #5 :Right Triangles
Find the perimeterof a right triangle with two legs of lengthand, respectively.
Not enough information provided
In order to find the perimeterof the right triangle, we need to first find the missing length of the hypotenuse. In order to find the length of the hypotenuse, use the Pythagorean Theorem:
, whereandare the lengths of the legs of the triangle, andis the length of the hypotenuse.
Substituting in our known values:
Now that we have all three sides of the right triangle, we can calculate the perimeter:
Example Question #1 :Properties Of Triangles
If aright triangle is similar to aright triangle, which of the other triangles must also be a similar triangle?
For the triangles to be similar, the dimensions of all sides must have the same ratio by dividing the 3-4-5 triangle.
The 6-8-10 triangle will have a scale factor of 2 since all dimensions are doubled the original 3-4-5 triangle.
The only correct answer that will yield similar ratios is thetriangle with a scale factor of 4 from the 3-4-5 triangle.
The other answers will yield different ratios.
Example Question #10 :Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3
What is the main difference between a right triangle and an isosceles triangle?
A right triangle has to have aangle and an isosceles triangle has to haveequal, base angles.
A right triangle has to have aangle and an isosceles triangle has to haveequal, base angles.
An isosceles triangle has to have a角和一个直角三角形equal, base angles.
A right triangle has to have aangle and an isosceles triangle has to haveequal, base angles.
A right triangle has to have aangle and an isosceles triangle has to haveequal, base angles.
A right triangle has to have aangle and an isosceles triangle has to haveequal, base angles.
By definition, a right triangle has to have one right angle, or aangle, and an isosceles triangle hasequal base angles and two equal side lengths.
Example Question #6 :Right Triangles
A right triangle has a hypotenuse of 39 and one leg is 36. What is the length of the other leg?
You may recognize these numbers as multiples of 13 and 12 (each by a factor of 3) and remember that sides of length 5, 12 and 13 make a special right triangle. So the other leg would be 15.
If you don't remember this, you can use Pythagorean theorem:
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