Question

3 The
given below.
sides of some triangles are
find out which ones are right angled triangled
a 11,12,15
b) 11, 60, 61​

Answer 1

Answer:

the answer is option A 11 12 15

Answer 2

Solution:

In order to find whether the given measures are sides of a right-angled triangle, we need to implement the Pythagoras theorem which is as follows:

$\sf{\implies\:Altitude^2+Base^2=Hypotenuse^2}$

We know that the hypotenuse is the longest side of a triangle and henceforth the largest measure in the option must be considered as hypotenuse while the other measures must be considered as the altitude and the base respectively.

a) 11, 12, 15

15 cm = Hypotenuse

12 cm = Altitude

11 cm = Base

LHS:

= Altitude² + Base²

= 12² + 11²

= 144 + 121

= 265

RHS:

= Hypotenuse²

= 15²

= 225

265 ≠ 225

Therefore these are not the measures of a right angled triangle.

b) 11, 60, 61

61 cm = Hypotenuse

60 cm = Altitude

11 cm = Base

LHS:

= Altitude² + Base²

= 60² + 11²

= 3600 + 121

= 3721

RHS:

= Hypotenuse²

= 61²

= 3721

LHS = RHS

Therefore there are the measures of a right angled triangle.

So,

Option B: 11, 60, 61 is the correct answer. ✔

Pythagoras theorem:

According to the Pythagoras theorem, the sum of the squares of the altitude and base of a right angles triangle is always equal to the square of the the length of the hypotenuse. The formula to be used is as follows:

$\sf{\implies\:Altitude^2+Base^2=Hypotenuse^2}$

Slight modifications in this equation will help us to find the measures of the other units as follows:

$\sf{\longrightarrow\:Altitude^2=Hypotenuse^2-Base^2}$

$\sf{\longrightarrow\:Base^2=Hypotenuse^2-Altitude^2}$