Egyptian Right Angles - Part 2

Since, each knot corresponds to $1$ unit length and there are $3$ and $5$ knots in the two ropes respectively, so the length of those two ropes are $3$ and $5$ units respectively.

For the three ropes to make a right triangle, the lengths of the ropes should make a pythagorean triplet. We know that $(3,4,5)$ make a pythagorean triplet as $5^2=3^2+4^2$ . Now, the two ropes have lengths $3,5$ respectively. To make the pythagorean triplet and make a right triangle, the third rope must have length $4$ units and since, each knot corresponds to $1$ unit length, so number of knots on the third rope $=\boxed{4}$ .

Assume the missing length is (b) By P.T b²=c²-a²

=5²-3²

=25-9

b²=16

=√16

=4 Answer :)

3,4,5 FORM A PYTHAGOREAN

3,4,5 FORM A PYTHAGOREAN TRIPLET

using pythagoras therom will be help full to solve the question

itz simple pythagoras theorem

hypotunese property

Its a simple Pythagorean Theorem. Instead of squares they use knots.

it must satisfy the relationship between the sides of any triangle which is a+b > and not equal to the remaining side of a triangle.....and since it is a right triangle therefore to find the remaining side it must satisfy the equation c^2 = a^2 + b^2 wherein: 5^2 = 3^2 + 4^2 :)

three squared plus four squared equals twenty-five, the square root of twenty-five is 5

simple, 5^2 = 3^2 + 4^2....,by phythogrous th.

3.4.5 are sides of right angle traingle

Pythagoras Theorem must be applied in this case.

A.T.Q 1 knot = 1 unit length Side 1 = 5 knots = 5 units Side 2 = 3 knots = 3 units Side 3 = Hypotenuse = x

x^2 = 5^2 * 3^2

x = 4 (on solving)

as distance between 2 knots are equal so that according to theorem 5^2-3^2=4^2 i.e. answer is 4

using pythagorus theorem for right angle traingle, x^2+3^2=5^2 => x=4

extremely simple since there are 5 and 3 knots so we know that the length is 5 and 3 units. now use basic middle-school algebra (pythagoras theorem) to get the answer simply as 5^2=x^2+3^2 solve and you get x=4