Question

If A is the area of a right angled triangle and b is one of the sides containing the right angle , then the length of attitude on the hypotenuse is

• A. $\frac{2Ab}{\sqrt{b^4+{4A}^2}}$
• B. $\frac{2A^{2}b}{\sqrt{b^4+{4A}^2}}$
• C. $\frac{2A{b}^2}{\sqrt{b^4+{4A}^2}}$
• D. $\frac{2A^2{b}^2}{\sqrt{b^4+A^2}}$

Answer 1

The correct option is A $\frac{2Ab}{\sqrt{b^4+{4A}^2}}$

We have,

Area of a right angle is $A$.

One side of right angle is $b$.

Then,

Area of triangle

$A=\frac{1}{2}\times b\times h$

$h=\frac{2A}{b}$

Using Pythagoras theorem,

${\left(\text{Hypotenous}\right)}^{\text{2}}\text{=}{\left(\text{Base}\right)}^{\text{2}}\text{+}{\left(\text{Height}\right)}^{\text{2}}$

$AC=\sqrt{b^2+\frac{4h^2}{b^2}}$

$AC=\sqrt{\frac{b^4+4h^2}{b^2}}$

$AC=\frac{1}{b}\sqrt{b^4+4h^2}$

Then,

Area of right angle containing Pythagoras theorem.

$A=\frac{1}{2}\times \frac{1}{b}\sqrt{b^4+4a^2}\times h$

$2Ab=\sqrt{b^4+4a^2}\times h$

$h=\frac{2Ab}{\sqrt{b^4+4a^2}}$

Hence, this is the answer.