Question

In the given figure, $\angle ABC={90}^{\circ }$ and $M$ is the mid-point of $AC$, $AB=8\text{cm}$ and $BC=6\text{cm}$. Then, choose the correct option(s).

• A. 3 cm
• B. 4 cm
• C. 5 cm
• D. 7 cm

Answer 1

Answer: (A), (B)

The correct options are
A

3 cm

B

4 cm

Using Pythagoras Theorem, $AC=\sqrt{8^2+6^2}=\sqrt{100}=10\text{cm}$

So, $AM=MC=5\text{cm}$
We know that the sum of two sides of a triangle is always greater than the third side.
Hence, in $△ABM$, $BM$ cannot be $14\text{cm}$ [as it is greater than the sum of $AB$ and $AM$
i.e. $8\text{cm}+5\text{cm}=13\text{cm}$].