Question

CD

is an altitude in right triangle ABC. The hypotenuse is 9 inches long, and

¯¯¯¯¯¯¯¯¯

AD

is 5 inches long as shown below.



What is the value of a?



7.5 inches

6.7 inches

6 inches

3 inches

Answer 1

a = 6 in

Explanation:

Using Pythagoras' Theorem
`a^2+b^2=c^2`, where a and b are the legs, and c is the hypotenuse of a right triangle.

`a^2+b^2=9^2`

`5^2+DC^2=b^2`

`4^2+DC^2=a^2`

`\implies 4^2+DC^2+5^2+DC^2=9^2`

`\implies 2 \ DC^2 =40`

`\implies DC^2=20`

If
`a^2=4^2+DC^2=16+20=36`

`\implies a=√(36) =6`