Question

A square is shown below. The length of the diagonal can be determined by using the Pythagorean theorem. Find the rational length of one of the sides that result in a rational hypotenuse. Also find an irrational length of one of the sides that result rational hypotenuse.

Answer 1

step 1

Find out the hypotenuse

Applying the Pythagorean Theorem

Let

H -----> hypotenuse

$\begin{gathered} H^2=s^2+s^2 \\ H^2=2s^2 \\ H=s\sqrt{2} \end{gathered}$

Part b

find an irrational length of one of the sides that result in the rational hypotenuse

For s=√2 -----> is an irrational number

but

H=√2*√2=2 -----> is a rational number

Part a

Find the rational length of one of the sides that result in a rational hypotenuse

Remember that

The product of a rational number and an irrational number is always irrational.

therefore

there is no rational number for one of the sides that result in a rational hypotenuse