10 grade maths> If ‘A’ is the area of a right triangle an...

If ‘A’ is the area of a right triangle and ‘b’ is one of the sides containing the right angle ,then prove that the length of the altitude on the hypotenuse is 2Ab/squrare root of b^2+4A^2

Ashok , 10 Years ago

Grade

2 Answers

Ajay Verma

Last Activity: 10 Years ago

soln:
altitude = d

area = ½ a*b =A = ½ d * (AB) …....................(1)

AB = (a²+b²)^1/2
= ( 4A²/b²+b²)^1/2

putting value on eqn1
A =½ d *( 4A²/b² +b²)^1/2

after solving
d = 2Ab / ( 4A²+ b²)^1/2

Regards

Sumit Majumdar

Last Activity: 10 Years ago

Dear student,
Let us assume a right angled triable ABC with the right angle being at B.
Let AB = b. Also let BC = c.

Hence we get:
$c=\frac{2A}{b}$
Also, using the Pythagoras theorem, we get:
$AC=\frac{\sqrt{b^{4}+4a^{2}}}{b}$
Hence, finding the area we get:
$\frac{1}{2}\frac{\sqrt{b^{4}+4a^{2}}}{b}BD=A\Rightarrow BD=\frac{2bA}{\sqrt{b^{4}+4a^{2}}}$
Regards
Sumit