Question

In the given figure, ∠ABC = ${90}^{\circ }$ and BM is a median, AB = 8 cm and BC = 6 cm. Then, choose the correct option(s).

• A. MC = 5 cm
• B. AM = 5 cm
• C. MB = 5 cm
• D. AC = 5 cm

Answer 1

Answer: (A), (B), (C)

The correct options are
A

MC = 5 cm

B

AM = 5 cm

C

MB = 5 cm

In triangle ABC, by applying pythagoras rule,

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

$A{C}^2=8^2+6^2=64+36$

$AC=\sqrt{64+36}=\sqrt{100}=10cm$

Since, M is the mid-point of AC,

$AM=MC=\frac{AC}{2}=\frac{10}{2}=5cm$

We know that in a right angled triangle, mid-point of the hypotenuse is always at equidistance from all the three vertices of the triangle.

$\Rightarrow$ AM = MC = MB = 5 cm