Question

The location of 'Home', 'Office' and 'Gym' of a person is shown above. If $\angle$ABC = 90${}^o$, the distance between office and gym is m.

• A. 55
• B. 65
• C. 70
• D. 75

Answer 1

The correct option is B 65

We know, the distance between office and gym is length AB in the triangle ABC.


Given, angle ∠ABC is 90${}^o$. So, triangle ABC is right-angled.
Using the Pythagorean theorem to find AB, we have:

$A{B}^2+B{C}^2=A{C}^2$

Substituting AC = 97 m and BC = 72 m in the equation,


$A{B}^2+{72}^2={97}^2$

$A{B}^2={97}^2-{72}^2$

$A{B}^2=9409-5184$

$A{B}^2=4225$

Taking square root,
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴ Distance between office and gym (AB) = 65 m