How can side be negative (Question:852343.0)

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kunal shinde

· started a discussion

· 1 Months ago

How can side be negative (Question:852343.0)

root 5 is greater than 1. Side will become negative

Question:

In the adjoining figure $\frac{A B}{B C} = \frac{A D}{D F}$ , where EBCF is a square. Find the ratio of $\frac{A E}{E F}$ .

Options:

$\frac{(1 \pm \sqrt{7})}{3}$

$\frac{(1 - \sqrt{7})}{2}$

$\frac{(1 + \sqrt{5})}{2}$

$\frac{(1 \pm \sqrt{5})}{2}$

Solution:

given that, $\frac{A B}{B C} = \frac{A D}{D F}$

Also, BC = BE.

Let,BE = x and AB = 1

Now, $\frac{A B}{B C} = \frac{A D}{D F} = \frac{1}{x + 1} = \frac{E F}{A E}$

or $\frac{A E}{E F} = \frac{x + 1}{x} = \frac{x}{1} \Rightarrow x + 1 = x^{2}$

or. x² – x – 1 = 0

$\Rightarrow$ x = $\frac{(1 \pm \sqrt{5})}{2}$

ratio can never be negative so correct answer is (c)

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How can side be negative (Question:852343.0)

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