Question

Which of the following cannot be sides of right angled triangle?
A) 9cm, 15cm, 12cm
B) 400mm,300mm, 500mm
C) 7cm,24cm,25cm
D) 9m,5m,7m
,​

Answer 1

D) 9m,5m,7m cannot be sides of right angled triangle .  

Answer 2

Correct Answer:

The correct answer for your question is Option-D = 9m, 5m, 7m.

Solution:

The main idea behind this question is Pythagoras Theorem. Let us see what this theorem states:

According to Pythagoras Theorem, the square of hypotenuse is equal to the sum of squares of other two sides of a right angled triangle.

Since, in a right angled triangle, we know that:

$\begin{gathered}\\\;\bf{\mapsto\;\;\red{Hypotenuse^2=Opposite\:side^2+Adjacent\:Side^2}}\end{gathered}$

This statement implies that Hypotenuse is greater than the other two sides.

Let's move on to each cases one by one:

Option-A:

$\begin{gathered}\\\;\bf{\rightarrow\;9cm,15cm,12cm}\end{gathered}$

According to Pythagoras Theorem,

$\begin{gathered}\\\;\bf{\rightarrow\;15^2=9^2+12^2}\end{gathered}$

$\begin{gathered}\\\;\bf{\rightarrow\;225=81+144}\end{gathered}$

$\begin{gathered}\\\;\red{\bf{\rightarrow\;225=225}}\end{gathered}$

Since, Pythagoras theorem is satisfied here, it is a right angled triangle.

Option-B:

$\begin{gathered}\\\;\bf{\rightarrow\;400mm,300mm,500mm}\end{gathered}$

According to Pythagoras Theorem,

$\begin{gathered}\\\;\bf{\rightarrow\;500^2=400^2+300^2}\end{gathered}$

$\begin{gathered}\\\;\bf{\rightarrow\;250000 = 160000+90000}\end{gathered}$

$\begin{gathered}\\\;\red{\bf{\rightarrow\;250000=250000}}\end{gathered}$

Since, Pythagoras theorem is satisfied here, it is a right angled triangle.

Option-C:

$\begin{gathered}\\\;\bf{\rightarrow\;7cm,24cm,25cm}\end{gathered}$

According to Pythagoras Theorem,

$\begin{gathered}\\\;\bf{\rightarrow\;25^2=7^2+24^2}\end{gathered}$

$\begin{gathered}\\\;\bf{\rightarrow\;625=49+576}\end{gathered}$

$\begin{gathered}\\\;\red{\bf{\rightarrow\;625=625}}\end{gathered}$

Since, Pythagoras theorem is satisfied here, it is a right angled triangle.

Option-D:

$\begin{gathered}\\\;\bf{\rightarrow\;9m,5m,7m}\end{gathered}$

According to Pythagoras Theorem,

$\begin{gathered}\\\;\bf{\rightarrow\;9^2=5^2+7^2}\end{gathered}$

According to Pythagoras Theorem,

$\begin{gathered}\\\;\bf{\rightarrow\;81=25+49}\end{gathered}$

$\begin{gathered}\\\;\orange{\bf{\rightarrow\;81=74}}\end{gathered}$

But we know that 81 will not be equal to 74.

Since, Pythagoras theorem is not satisfied here, it is not a right angled triangle.

Hence, our correct answer is Option-D