Question

Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle

• A. $3\mathrm{cm},4\mathrm{cm},6\mathrm{cm}$
• B. $9\mathrm{cm},16\mathrm{cm},26\mathrm{cm}$
• C. $1.5\mathrm{cm},3.6\mathrm{cm},3.9\mathrm{cm}$
• D. $7\mathrm{cm},24\mathrm{cm},26\mathrm{cm}$

Answer 1

The correct option is C

$1.5\mathrm{cm},3.6\mathrm{cm},3.9\mathrm{cm}$

Explanation for the correct options:

Option (C): $1.5\mathrm{cm},3.6\mathrm{cm},3.9\mathrm{cm}$

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse,$c$ is equal to the sum of the squares of the other two sides $a,b$.

i.e. $c^2=a^2+b^2$

Consider, $1.5\mathrm{cm},3.6\mathrm{cm},3.9\mathrm{cm}$ compare the value with values $a,b,$ and $c$:

$a=1.5,b=3.6,c=3.9$

Apply value into the above-given formula:

$$\begin{gathered} 3.9^2=1.5^2+3.6^2 \\ \Rightarrow 15.21=2.25+12.96 \\ \therefore 15.21=15.21 \end{gathered}$$

Hence, option $\mathrm{C}$ is correct .

Option (A): $3\mathrm{cm},4\mathrm{cm},6\mathrm{cm}$

Consider, $3\mathrm{cm},4\mathrm{cm},6\mathrm{cm}$ compare the value with values $a,b,$ and $c$:

$a=3,b=4,c=6$

Apply value into the above-given formula:

$$\begin{gathered} 6^2=3^2+4^2 \\ \Rightarrow 36=9+16 \\ \therefore 36\ne 25 \end{gathered}$$

Hence, option $A$ is in-correct .

Option (B): $9\mathrm{cm},16\mathrm{cm},26\mathrm{cm}$

Consider $9\mathrm{cm},16\mathrm{cm},26\mathrm{cm}$comparing the value with values $a,b,$ and $c$:

$a=9,b=16,c=26$

Apply value into the above-given formula:

$$\begin{gathered} {26}^2=9^2+{16}^2 \\ \Rightarrow 676=81+256 \\ \therefore 676\ne 337 \end{gathered}$$

Hence, option $B$ is in-correct .

Option (D): $7\mathrm{cm},24\mathrm{cm},26\mathrm{cm}$

Consider, $7\mathrm{cm},24\mathrm{cm},26\mathrm{cm}$ compare the value with values $a,b,$ and $c$:

$a=7,b=24,c=26$

Apply value into the above-given formula:

$$\begin{gathered} {26}^2=7^2+{24}^2 \\ \Rightarrow 676=49+576 \\ \therefore 676\ne 625 \end{gathered}$$

Hence, option $D$ is in-correct .

Hence, the correct choice is option $\mathrm{C}$.