Question

The length of 3 sides of a triangle are, 6cm, 8cm and 10cm. The length of the median to the greatest side is then,

Answer 1

median to the hypotenus in a right triangle is half of the hypotenus...hope u understand..regards

Answer 2

Answer: The length of the median to the greatest side will be 5cm.

Step-by-step explanation:

Given that:

• length of 3 sides of the triangle are 6cm, 8cm and 10cm.

We have to find the median to the greatest side that is 10cm here.

Finding the median:

Greatest side is 10 cm here.

Other two sides are also given.

Applying the Pythagoras theorem to the three sides of the triangle, we get;

• $a^{2}+b^{2} =c^{2}$

where, a, b and c are the sides of the right angle triangle.

Putting values of three sides given;

$(6)^{2} +(8)^{2} =(10)^{2}$

By solving;

$36+64=100$

Hence, L.H.S=R.H.S

Therefore, the greatest side that is 10cm is hypotenuse to the right angle triangle in this case.

Now, we know that:

• median=hypotenuse/2

• median, $m=\frac{h}{2}$

Putting the values from the question, we get;

$m=\frac{10}{2} =5cm$

Hence, the median to the greatest side is 5cm.