GMAT Math : Triangles
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Example Questions
Example Question #2 : Dsq: Calculating The Area Of A Right Triangle
Find the area of the right triangle.
Statement 1): The hypotenuse is 
Statement 2): Both legs have a side length of 
BOTH statements taken TOGETHER are sufficient to answer the question, but neither statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statement 2) ALONE is sufficient, but Statement 1) ALONE is not sufficient to answer the question.
BOTH statements TOGETHER are NOT sufficient, and additional data is needed to answer the question.
Statement 1) ALONE is sufficient, but Statement 2) ALONE is not sufficient to answer the question.
Statement 2) ALONE is sufficient, but Statement 1) ALONE is not sufficient to answer the question.
Statement 1) only provides the hypotenuse of the triangle, but it does not imply that both legs of the right triangle are congruent sides. Of the three interior angles, only the right angle is known with the other 2 unknown interior angles.
Statement 1) does not have enough information to solve for the area of the triangle.
Statement 2) provides the lengths of both legs. The formula 
Statement 2) can be used by itself to solve for the area of the triangle.
Example Question #3 : Dsq: Calculating The Area Of A Right Triangle
The lobby of a building is in the shape of a right triangle. The shortest side of the room is 
I) Each tile covers 
II) The longest side of the lobby is five less than three times the shortest side.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
Both statements are needed to answer the question.
Either statement is sufficient to answer the question.
Both statements are needed to answer the question.
To find the number of tiles needed, we need to find the area of the lobby and the area of one tile.
I) Gives us the area of one tile.
II) Gives us the length of the hypotenuse of the lobby.
Use II) along with the info given in the question to find the last side (Pythagorean Theorem).
From there you can find the area of the lobby.
Use I) along with the area of the lobby to find the number of tiles needed.
Example Question #4 : Dsq: Calculating The Area Of A Right Triangle
What is the area of the right triangle?
- The hypotenuse measures
.
- The height measures
.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Neither statement provides us with sufficient information to answer the question but both statements taken together are sufficient to answer the question.
In order to find the area of the right triangle we need both the height and base. We can use the Pythagorean Theorem to solve for the base.
Now we can find the area:
Example Question #181 : Triangles
What is the perimeter of isosceles triangle ABC?
(1)
(2)
Statement 2 ALONE is sufficient to answer the question, but the other statement alone is not sufficient.
EACH statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are not sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but the other statement alone is not sufficient.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
BOTH statements TOGETHER are not sufficient to answer the question.
(1) This statement gives us the length of one side of the triangle. This information is insufficient to solve for the perimeter.
(2) This statement gives us the length of one side of the triangle. This information is insufficient to solve for the perimeter.
Additionally, since we don't know which one of the sides (
Example Question #2 : Dsq: Calculating The Perimeter Of A Right Triangle
Find the perimeter of right triangle 
I)
II)
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Either statement is sufficient to answer the question.
Both statements are needed to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Both statements are needed to answer the question.
If the two shorter sides of a right triangle are equal, that means our other two angles are 45 degrees. This means our triangle follows the ratios for a 45/45/90 triangle, so we can find the remaining sides from the length of the hypotenuse.
I) Tells us we have a 45/45/90 triangle. The ratio of side lengths for a 45/45/90 triangle is 
II) Tells us the length of the hypotenuse.
Together, we can find the remaining two sides and then the perimeter.
Example Question #3 : Dsq: Calculating The Perimeter Of A Right Triangle
Find the perimeter of the right triangle.
- The product of the base and height measures
.
- The hypotenuse measures
.
Each statement alone is sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 1: We need additional information.
But this can mean our base and height measure 2 and 24, 4 and 12, or 6 and 8.
We cannot determine which one based solely on this statement.
Statement 2: We're given the length of the hypotenuse so we can narrow down the possible base and height values.
We have to see which pair of values makes the statement 
The only pair that does is 6 and 8.
We can now find the perimeter of the right triangle:
or, if you're more familiar with the equation 
Example Question #4 : Dsq: Calculating The Perimeter Of A Right Triangle
Calculate the perimeter of the triangle.
- The hypotenuse of the right triangle is
.
- The legs of the right triangle measure
and
.
Each statement alone is sufficient to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statement 1: In order to find the perimeter of a right triangle, we need to know the lengths of the legs, not the hypotenuse.
Statement 2: Since we have the values to both of the legs' lengths, we can just plug it into the equation for the perimeter:
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