Question

Which of the following are not the sides of a right angled triangles

• A. 9cm, 15cm, 12cm
• B. 2cm, 1cm, $\sqrt{5}$cm
• C. 9cm, 5cm, 7cm
• D. 40cm, 30cm, 50 cm

Answer 1

The correct option is C 9cm, 5cm, 7cm

In the Right-angled triangle square of the hypotenuse is equal to the sum of the square of the base and perpendicular and hypotenuse is the longest side of the triangle.

$\therefore H^2=B^2+P^2$

In option A

B=9 cm,H=15 cm,P=12cm

$\therefore H=\sqrt{9^2+{12}^2}$

$\Rightarrow H=\sqrt{81+144}$

$\Rightarrow H=\sqrt{225}$

$\Rightarrow H=15cm$

Hence this is the side of Right angled triangle.

In option B

B=1 cm,H$=\sqrt{5}$cm,P=2cm

$\therefore H=\sqrt{1^2+2^2}$

$\Rightarrow H=\sqrt{1+4}$

$\Rightarrow H=\sqrt{5}$

Hence these are the side of Right angled triangle.

In option C

B=5 cm,H$=9$cm,P=7cm

$\therefore H=\sqrt{5^2+7^2}$

$\Rightarrow H=\sqrt{25+49}$

$\Rightarrow H=\sqrt{74}$

Here H $\ne 9$ then these are not the side of a right angled triangle