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The area of isosceles right triangle XYZ equals 9. Which of

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The area of isosceles right triangle XYZ equals 9. Which of [#permalink] New post 26 Jun 2020, 00:53
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The area of isosceles right triangle XYZ equals 9. Which of the following could be the perimeter?

I. 12

II. 13 + √145

III. 6√2 + 6

(A) I only

(B) I and III

(C) III only

(D) I and II

(E) All of the above
[Reveal] Spoiler: OA

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Re: The area of isosceles right triangle XYZ equals 9. Which of [#permalink] New post 26 Jun 2020, 06:45
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Farina wrote:
The area of isosceles right triangle XYZ equals 9. Which of the following could be the perimeter?

I. 12

II. 13 + √145

III. 6√2 + 6

(A) I only

(B) I and III

(C) III only

(D) I and II

(E) All of the above


Here's what an isosceles right triangle looks like:
Image

Given: The area = 9

Area of triangle = (base)(height)/2

So we can write: (x)(x)/2 = 9
Multiply both sides of the equation by 2 to get: x² = 18
Solve: x = √18
Simplify: x = 3√2

So our triangle looks like this:
Image
Aside: If x = 3√2, then (√2)(x) = (√2)(3√2) = 6

Perimeter = 3√2 + 3√2 + 6 = 6√2 + 6

Answer: C

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Brent
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Re: The area of isosceles right triangle XYZ equals 9. Which of   [#permalink] 26 Jun 2020, 06:45
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The area of isosceles right triangle XYZ equals 9. Which of

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