Question

The lenghts of the sides of a triangle are 9 cm 12 cm and 15 cm then the length of the median to the longest side is

• A. 7.2 cm
• B. 7.3 cm
• C. 7.4 cm
• D. 7.5 cm

Answer 1

The correct option is D 7.5 cm

Given length of the sides of triangle are 9 cm,12 cm and 15 cm

We know that median=$\frac{\sqrt{2b^2+2c^2-a^2}}{2}$

Here a=15 cm b=12 cm and c=9 cm

Then median of longest side=$\frac{\sqrt{2(12{)}^2+2(9{)}^2-(15{)}^2}}{2}=\frac{\sqrt{288+162-225}}{2}\Rightarrow =\frac{\sqrt{225}}{2}=\frac{15}{2}=7.5$ cm