Question

The sides of a triangle are of lengths $20,21$ and $29$ units. The sum of the lengths of altitudes will be ?

• A. $1609/29$ units
• B. $49$ units
• C. $1609/21$ units
• D. $70$ units

Answer 1

The correct option is A $1609/29$ units

The sides of triangle are $20,21,29$.

The given triangle is right angles triangle with $29$ as hypotenuse.

Let the length of altitudes be $a,b,c$

We can say that $a=20,b=21$, since it is right angled triangle and $c$ is the length of altitude to the hypotenuse

By equating area, we get $\frac{1}{2}\times 20\times 21=\frac{1}{2}\times 29\times c$

$\Rightarrow c=\frac{420}{29}$

Therefore the lengths of altitudes will be $a+b+c=20+21+\frac{420}{29}=\frac{1609}{29}$

So the correct option is A.