question_answer

The sides of a triangle are 30, 70 and 80 units. If an altitude is droped upon the side of length 80 units, the larger segment cut off on this side is:

A) 62 units

B) 63 units

C) 64 units

D) 65 units

Correct Answer: D

Solution :

[d]

Now        \[{{h}^{2}}={{30}^{2}}-{{(80-x)}^{2}}\]

Also        \[{{h}^{2}}={{70}^{2}}-{{x}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,{{30}^{2}}-{{(80-x)}^{2}}={{70}^{2}}-{{x}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,160x=10400\Rightarrow x=65\]units.