Question

In $\Delta STU.m\angle S+m\angle T=m\angle U$ $SU=8$ and $TU=15$. Then the length of the median through vertex $U$ is ..........

• A. $7.5$
• B. $5.5$
• C. $15$
• D. $8.5$

Answer 1

The correct option is D $8.5$

$\angle S+\angle T=\angle U$

and $\angle S+\angle T+\angle U={180}^o$

So, $\angle U+\angle U={180}^o\Rightarrow \angle U={90}^o$

Hence, it is a Right angled Triangle

Also, $S{U}^2+T{U}^2=S{T}^2\Rightarrow 8^2+{15}^2=S{T}^2\Rightarrow ST=17$

We know that,

The median on the hypotenuse of a right triangle divides the triangle into two isosceles triangles, because the median equals one-half the hypotenuse

Hence, Length of Median $=\frac{17}{2}=8.5$