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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
The perimeter of a certain isosceles right triangle is 16 + 16 (2)^1/2
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10 Apr 2022, 04:08
10 Apr 2022, 04:08
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The perimeter of a certain isosceles right triangle is \(16 + 16 \sqrt{2}\). What is the length of the hypotenuse of the triangle?
(A) \(8\)
(B) \(16\)
(C) \(4\sqrt{2}\)
(D) \(8\sqrt{2}\)
(E) \(16\sqrt{2}\)
(A) \(8\)
(B) \(16\)
(C) \(4\sqrt{2}\)
(D) \(8\sqrt{2}\)
(E) \(16\sqrt{2}\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The perimeter of a certain isosceles right triangle is 16 + 16 (2)^1/2
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10 Apr 2022, 06:08
10 Apr 2022, 06:08
2
GeminiHeat wrote:
The perimeter of a certain isosceles right triangle is \(16 + 16 \sqrt{2}\). What is the length of the hypotenuse of the triangle?
(A) \(8\)
(B) \(16\)
(C) \(4\sqrt{2}\)
(D) \(8\sqrt{2}\)
(E) \(16\sqrt{2}\)
(A) \(8\)
(B) \(16\)
(C) \(4\sqrt{2}\)
(D) \(8\sqrt{2}\)
(E) \(16\sqrt{2}\)
An IMPORTANT point to remember is that, in any isosceles right triangle, the sides have length x, x, and x√2 for some positive value of x.
Note: x√2 is the length of the hypotenuse, so our goal is to find the value of x√2
From here, we can see that the perimeter will be x + x + x√2
In the question, the perimeter is 16 + 16√2, so we can create the following equation:
x + x + x√2 = 16 + 16√2
Simplify: 2x + x√2 = 16 + 16√2
IMPORTANT: Factor x√2 from the left side to get : x√2(√2 + 1) = 16 + 16√2
Now factor 16 from the right side to get: x√2(√2 + 1) = 16(1 + √2)
Divide both sides by (1 + √2) to get: x√2 = 16
Answer = B
Cheers,
Brent
The perimeter of a certain isosceles right triangle is 16 + 16 (2)^1/2
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10 Apr 2022, 16:15
10 Apr 2022, 16:15
This question has two critical points:
1) Students must recall that hypotenuse (isosceles right triangle) = L√2
2) Solve this 2L+L√2 = 16+16√2
If you get these points, it´s piece of cake!
1) Students must recall that hypotenuse (isosceles right triangle) = L√2
2) Solve this 2L+L√2 = 16+16√2
If you get these points, it´s piece of cake!
