Question

Find the length of the altitude drawn to the hypotenuse. The triangle is not to scale.

Answer 1

D is the correct option.

Explanation:

Let us apply the Pythagorean theorem in the right angle triangles.

In right angle triangle ABC

`24^2=AB^2+AC^2......(1)`

Now, in right angle triangle ABD,

`AB^2=AD^2+4^2\\AB^2=AD^2+16.......(2)`

Now, in right angle triangle ADC,

`AC^2=AD^2+20^2\\\\AC^2=AD^2+400`

From equation (1) and (2)

`24^2-AB^2=AD^2+400\\\\24^2-(AD^2+16)=AD^2+400\\\\576-AD^2-16=AD^2+400\\\\2AD^2=160\\\\AD^2=80\\\\AD=4√(5)`