The following figure is known as the
Ailles rectangle:
The figure above illustrates the following:
In a 15-75-90 triangle, (shorter leg)/(hypotenuse) = (√3 - 1)/(2√2).
Mo2men wrote:In triangle ABC, if angle ABC is 30 degrees, AC = 2 * √2 and AB = BC = X, what is the value of X?
A) √3 - 1
B) √3 + 2
C) (√3 - 1) / 2
D) (√3 + 1) / 2
E) 2 * (√3 + 1)
If we split the given triangle in half, the following figure is yielded:
In the 15-75-90 triangle on the right, the shorter leg = √2 and the hypotenuse = X.
Since (shorter leg)/(hypotenuse) = (√3 - 1)/(2√2), we get:
(√2)/X = (√3 - 1)/(2√2)
X(√3 - 1) = (√2)(2√2)
X(√3 - 1) = 4
X = 4/(√3 - 1)
X = [4(√3 + 1)] / [(√3 - 1)(√3 + 1)]
X = [4(√3 + 1)] / (3 - 1)
X = [4(√3 + 1)] / 2
X = 2(√3 + 1).
The correct answer is
E.
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