Question

The length of hypotenuse of a right angled triangle is 15 cm. Find the length
of median of its hypotenuse.

Answer 1

Answer:

Length of hypotenuse = 15 [Given]

Length of median on the hypotenuse = 1/2 x length of hypotenuse

[In a right angled triangle, the length of the median on the hypotenuse is half the length of the hypotenuse] = (1/2) x 15 = 7.5 ∴ The length of the median on the hypotenuse is 7.5 units

Answer 2

et us start the solution to the above question by drawing the diagram of the situation given in the question.

For the right angled triangle given in the question, the hypotenuse is equal to 15cm, one of the sides is 6cm less than the hypotenuse, i.e., 15-6=9 cm which is shown in the above diagram.

Now we will apply Pythagoras's theorem in ΔABC .

(perpendicular)2+(base)2=(hypotenuse)2

⇒AB2+92=152

⇒AB2=152−92

Now, we know that 152=225 and 92=81 . If we put this in the above equation, we get

AB2=225−81

⇒AB2=144

Now, we will take root on both sides of the equation. On doing so, we get

AB=144−−−√=12cm

So, the correct answer is “Option A”.

Note: In the question, the key is the diagram and the constructions. The other point to remember is that AB2=144 actually implies AB=±144−−−√=±12cm , but we have considered only one value because the length of a side cannot be negative, so only positive value can be the side length. The other point is you must remember the squares of the natural numbers till 20, as they are used very often.