DSQ: Calculating the perimeter of a right triangle - GMAT Quantitative Reasoning
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What is the perimeter of isosceles triangle ABC?
(1) 
(2) 
What is the perimeter of isosceles triangle ABC?
(1)
(2)
(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 (
or 
) is one of the equal sides, it's impossible to determine the perimeter given the information provided.
(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 (
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Find the perimeter of right triangle 
.
I) 
II) 
Find the perimeter of right triangle
I)
II)
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.
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.
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Find the perimeter of the right triangle.
- The product of the base and height measures
.
- The hypotenuse measures
.
Find the perimeter of the right triangle.
- The product of the base and height measures
- The hypotenuse measures
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 
true.
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 
, then:
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
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Calculate the perimeter of the triangle.
- The hypotenuse of the right triangle is
.
- The legs of the right triangle measure
and 
.
Calculate the perimeter of the triangle.
- The hypotenuse of the right triangle is
- The legs of the right triangle measure
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:
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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