Question

If $AB=28$ cm and $BC=45$ cm, what is the length in centimetres of $AC$?

• A. $35$ cm.
• B. $45$ cm.
• C. $53$ cm.
• D. $64$ cm.

Answer 1

The correct option is C $53$ cm.

SInce the three angles of a triangle add up to ${180}^o,38.5+51.5+\angle ABC={180}^o$

$\therefore \angle ABC={90}^o$

Since $\angle ABC={90}^o,(AB{)}^2+(BC{)}^2=(AC{)}^2$

$\Rightarrow (28{)}^2+(45{)}^2=(AC{)}^2$

i.e. $(AC{)}^2=784+2025=2809$

$\Rightarrow AC=53$ cm