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15 Aug 2019, 00:28
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (01:00) correct
30%
(01:04)
wrong
based on 63
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A right triangle has two legs of equal length. What is the perimeter, in centimeters, of the triangle?
(1) The area of the triangle is 4 square centimeters.
(2) The hypotenuse of the triangle measures 4 cm.
(1) The area of the triangle is 4 square centimeters.
(2) The hypotenuse of the triangle measures 4 cm.
15 Aug 2019, 07:08
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It's an isosceles right triangle, or a 45-45-90 triangle. There's only one 45-45-90 triangle with an area of 4, and there's only one 45-45-90 triangle with a hypotenuse of 4. So the answer must be D; there's no need to calculate anything.
17 Sep 2019, 05:14
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SajjadAhmad
Official Explanation
The only way for a right triangle to have two sides of equal length is to be a 45-45-90 triangle. That means that the lengths of the sides of this triangle are in the ratio \(x:x:\sqrt{2}\). On to the statements, separately first.
Statement (1) gives us the area of the triangle. Since the two sides of length x are perpendicular, they are valid base-height pair. Therefore, bh/2 = x^2/2 = 4. That allows us to solve for x (it's \(2\sqrt{2}\)). From there, we can determine the lengths of all of the sides and hence the perimeter. Statement (1) is sufficient.
Statement (2) tells us that \(x\sqrt{2}=4\), so we can solve for x and determine the perimeter of the triangle. Statement (2) is therefore sufficient and the correct answer is (D).
We see in this question that special triangles, like circles, are prone to sufficiency, because they are defined by a small number of parameters.
Again, the correct answer is (D).
