Question

In a right-angled triangle $△ABC$, length of two sides are $8cm$ and $6cm$, then which of the following statement/s is/are correct?

• A. Length of greatest side is $10cm$
• B. $\angle ACB>{90}^o$
• C. $\angle BAC<{90}^o$
• D. Pythagoras theorem is not applicable here

Answer 1

Answer: (A), (C)

The correct options are
A Length of greatest side is $10cm$
C $\angle BAC<{90}^o$

$\Delta ABC$ is a given triangle
$\angle ABC={90}^{\circ },AB=6cm,BC=8cm$ .
Now, AC $=\sqrt{{AB}^2+{BC}^2}=\sqrt{8^2+6^2}=10cm$ .
It is the hypotenuse of the $△ABC$.
Option A $\Rightarrow$ The statement is correct because $AC>AB$ and $AC>BC$ from the above findings.
Option B $\Rightarrow$ The statement is wrong because $\angle ABC+\angle CAB+\angle ACB={180}^{\circ }$.
But, $\angle ABC={90}^{\circ }$ given.
Therefore, $\angle ACB+\angle CAB={180}^{\circ }-{90}^{\circ }={90}^{\circ }$.
So each of $\angle ACB,\angle CAB$ is less than ${90}^{\circ }$.
Option C $\Rightarrow$ The statement is true according to the reasoning for the statement in B option.
Option D $\Rightarrow$ The statement is wrong because given triangle is a right angled triangle and Pythagoras theorem is always applicable to right triangles.