Question

Measures of the sides of four triangles are given. The triangle which is not a right angled triangle is
?
A)3cm, 4cm, 5cm

B)9cm, 12cm, 15cm

C)3cm, 5cm, 7cm

D)30cm, 40cm, 50cm​

Answer 1

Solution:

To find the triangle which doesn't form a right-angled triangle, we must implement the Pythagoras theorem which is stated below:

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

A) 3cm, 4cm, 5cm

Here, the highest measure will be taken as the hypotenuse and the other two measures will be taken as the altitude and base.

➡ Hypotenuse = 5 cm

➡ Altitude = 4 cm

➡ Base = 3 cm

Applying the formula:

Hypotenuse² = 4² + 3²

Hypotenuse² = 16 + 9

Hypotenuse² = 25

Hypotenuse = √25

Hypotenuse = 5 cm

This is the same value as mentioned in the options.

∴ 3cm, 4cm and 5cm are measures of a right-angled triangle.

B) 9cm, 12cm, 15cm

Here, the highest measure will be taken as the hypotenuse and the other two measures will be taken as the altitude and base.

➡ Hypotenuse = 15 cm

➡ Altitude = 12 cm

➡ Base = 9 cm

Applying the formula:

Hypotenuse² = 12² + 9²

Hypotenuse² = 144 + 81

Hypotenuse² = 225

Hypotenuse = √225

Hypotenuse = 15 cm

This is the same value as mentioned in the options.

∴ 9cm, 12cm and 15cm are sides of a right-angled triangle.

C) 3cm, 5cm, 7cm

Here, the highest measure will be taken as the hypotenuse and the other two measures will be taken as the altitude and base.

➡ Hypotenuse = 7 cm

➡ Altitude = 5 cm

➡ Base = 3 cm

Applying the formula:

Hypotenuse² = 5² + 3²

Hypotenuse² = 25 + 9

Hypotenuse² = 34

Hypotenuse = √34

√34 ≠ 7

The measurements in the options do not abide by the result.

∴ 3cm, 5cm and 7cm are not the sides of a right angled triangle.

D) 30cm, 40cm, 50cm

Here, the highest measure will be taken as the hypotenuse and the other two measures will be taken as the altitude and base.

➡ Hypotenuse = 50 cm

➡ Altitude = 40 cm

➡ Base = 30 cm

Applying the formula:

Hypotenuse² = 40² + 30²

Hypotenuse² = 1600 + 900

Hypotenuse² = 2500

Hypotenuse = √2500

Hypotenuse = 50 cm

This is the same value as mentioned in the options.

∴ 30cm, 40cm and 50cm are sides of a right-angled triangle.

Hence, the required correct option is

Option C: 3cm, 5cm, 7cm ✔