Question

In the diagram below, BC is an altitude of AABD. To the nearest whole unit, what is the length of CD? ​

Answer 1

C

Explanation:

Using the Pythagorean theorem, find BA:
`\sqrt{37^(2)+53^(2) } = √(4178)`

Making BC = x, find the lenth of BD:
`\sqrt{x^(2) +37^(2) }`

Since DBA is a right triangle, this follows:
`DA^(2)=BD^(2)+BA^(2)`

Substitute:
`(x+53)^(2) =√(4178) ^(2) +√(x^2+37^2) ^(2)`

Expand:
`x^(2) +106x+2809=x^(2) +5547`

Solve: 106x = 2736

Finally: x ≈ 25.8 ≈ 26

Therefore: C