Question

Which of the following can't be the lengths of the sides of a right-angled triangle?

• A. $5$ inches, $12$ inches, $13$ inches
• B. $\frac{1}{3}$ of a foot, $\frac{1}{4}$ of a foot, $\frac{1}{5}$ of a foot
• C. $9$cm, $40$cm, $41$cm
• D. $\frac{3}{4}$ of a foot, $1$ foot, $15$ inches

Answer 1

The correct option is B $\frac{1}{3}$ of a foot, $\frac{1}{4}$ of a foot, $\frac{1}{5}$ of a foot

For a set of numbers to be sides of a right angled triangle, the square of the longest side must equal the sum of the squares of the other two sides.

In option A, ${13}^2=169,5^2+{12}^2=169$ so possible.

In option B, ${\left(\frac{1}{3}\right)}^2=\frac{1}{9},{\left(\frac{1}{4}\right)}^2+{\left(\frac{1}{5}\right)}^2=\frac{41}{400}$

Since, these two values are not equal, this set cannot form a right angled triangle.