In a right angled triangle with sides a and b and hypotenuse c,

Question:

In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Solution:

Let $\triangle \mathrm{ABC}$ be a right angle triangle having sides $a$ and $b$; and hypotenuse $c . \mathrm{BD}$ is the altitude drawn on the hypotenuse AC.

Since the altitude is perpendicular on the hypotenuse, both the triangles are similar

$\frac{A B}{B D}=\frac{A C}{B C}$

$\frac{a}{x}=\frac{c}{b}$

$x c=a b$

Hence, $a b=c x$.

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