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Area of Right angle Triangle (DS)

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by ceilidh.erickson » Sat Apr 12, 2014 1:21 pm
In order to find the area of a triangle, we need the base and the height. For a right triangle, that means the lengths of both the two non-hypotenuse sides.

Statements (1) and (2) are clearly insufficient on their own, as each gives us only a single side length, and we need both the base and the height.

Be careful, though! That doesn't mean that using the statement together will give us the area. This question is trying to trick us into thinking that we have a familiar right triangle: 9-12-15, giving us an area of 54.

That's one possibility, but it's also possible that 9 and 15 are the base and height, and the hypotenuse is sqrt(306). This would give us an area of 67.5.

The answer is E.

Remember that in geometry DS questions, you should try to think of as many configurations of the given shape as possible - don't just assume that it's the familiar one.
Ceilidh Erickson
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Harvard Graduate School of Education
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Area of Right angle Triangle (DS)

by Brent@GMATPrepNow » Sat Apr 12, 2014 1:27 pm
ajaysingh24 wrote:What is the area of right triangle XYZ?

(1) Side YZ is 9 inches long.
(2) Side XZ is 15 inches long.
Target question: What is the area of right triangle XYZ?

KEY CONCEPT: Area of triangle = (1/2)(base)(height)
So, to answer the target question, we need lengths of BOTH the base AND the height.

Statement 1: Side YZ is 9 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Side XZ is 15 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We still don't have enough information.
Consider the following 2 cases (which both satisfy the given conditions).

case a:
Image
Here, the area = (1/2)(9)(12) = 54

case b:
Image
Here, the area = (1/2)(9)(15)= 67.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sun Apr 29, 2018 5:19 am, edited 1 time in total.
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by gmattesttaker2 » Sun Jun 22, 2014 6:04 pm
Brent@GMATPrepNow wrote:
ajaysingh24 wrote:What is the area of right triangle XYZ?

(1) Side YZ is 9 inches long.
(2) Side XZ is 15 inches long.
Target question: What is the area of right triangle XYZ?

KEY CONCEPT: Area of triangle = (1/2)(base)(height)
So, to answer the target question, we need lengths of BOTH the base AND the height.

Statement 1: Side YZ is 9 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Side XZ is 15 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We still don't have enough information.
Consider the following 2 cases (which both satisfy the given conditions).

case a:
Image
Here, the area = (1/2)(9)(12) = 54

case b:
Image
Here, the area = (1/2)(9)(15)= 67.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Hello Brent,

Thanks for the explanation. Suppose we have a right angled triangle where we are given the value of the hypotenuse only and are asked to determine the value of the other two sides, is it possible to determine those values? For example, if the hypotenuse of a right triangle is 5, then I think we can say for sure that the value of the other 2 sides are 3 and 2. Can we do this for any right triangle if we know the hypotenuse? Thanks a lot for your help.

Best Regards,
Sri

I could be wrong but I think I have come across triangles hwere
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by Brent@GMATPrepNow » Sun Jun 22, 2014 6:32 pm
gmattesttaker2 wrote: Hello Brent,

Thanks for the explanation. Suppose we have a right angled triangle where we are given the value of the hypotenuse only and are asked to determine the value of the other two sides, is it possible to determine those values? For example, if the hypotenuse of a right triangle is 5, then I think we can say for sure that the value of the other 2 sides are 3 and 2. Can we do this for any right triangle if we know the hypotenuse? Thanks a lot for your help.

Best Regards,
Sri

I could be wrong but I think I have come across triangles hwere
If we know the length of the hypotenuse only, then we can't find the other two lengths.
For example, if the hypotenuse has length 5 and the other two sides have lengths x and y, all we can say for certain is that x² + y² = 5² (by the Pythagorean Theorem)
There is an infinite number of solutions to this equation. Here are just a few:
x = 3 and y = 4
x = √11 and y = √14
x = √8 and y = √17
x = 2 and y = √21
etc.

Cheers,
Brent
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by gmattesttaker2 » Sun Jun 22, 2014 8:21 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote: Hello Brent,

Thanks for the explanation. Suppose we have a right angled triangle where we are given the value of the hypotenuse only and are asked to determine the value of the other two sides, is it possible to determine those values? For example, if the hypotenuse of a right triangle is 5, then I think we can say for sure that the value of the other 2 sides are 3 and 2. Can we do this for any right triangle if we know the hypotenuse? Thanks a lot for your help.

Best Regards,
Sri

I could be wrong but I think I have come across triangles hwere
If we know the length of the hypotenuse only, then we can't find the other two lengths.
For example, if the hypotenuse has length 5 and the other two sides have lengths x and y, all we can say for certain is that x² + y² = 5² (by the Pythagorean Theorem)
There is an infinite number of solutions to this equation. Here are just a few:
x = 3 and y = 4
x = √11 and y = √14
x = √8 and y = √17
x = 2 and y = √21
etc.

Cheers,
Brent

Hello Brent,

Thanks a lot for the clarification.

Best Regards,
Sri
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