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Introduction to Similar Triangles

What is the v...

Question

What is the value of x in the figure if BD < DC?

4

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Solution

The correct option is A 4
From this figure, we can write
$B D \times D C = A D^{2}$

$∴ x (13 - x) = 6^{2} = 36 \Rightarrow 13 x - x^{2} = 36 \Rightarrow x^{2} - 13 x + 36 = 0 \Rightarrow x^{2} - 4 x - 9 x + 36 = 0 \Rightarrow x (x - 4) - 9 (x - 4) = 0 \Rightarrow (x - 4) (x - 9) = 0 \Rightarrow x = 4 o r x = 9$

Since BD is small in this figure, x = 4 is the appropriate answer.

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