The ancient Egyptians had a neat way to construct right angles. They would make a long rope with knots to make 121212 equal sections.

When they stretched the rope into the triangle shown below, they always got a right angle. This was useful when planning the pyramids, for example.

If we apply the Pythagorean Theorem to the Egyptian knots we can see that 3^2 + 4^2 = 5^23
2
+4
2
=5
2
3, squared, plus, 4, squared, equals, 5, squared.
Which of the sets of three numbers listed would also let you form a right angle in this way?
Choose all answers that apply:
Choose all answers that apply:

(Choice A, Incorrect)
INCORRECT
\text{\{1, 1, 1\}}{1, 1, 1}start text, left brace, 1, comma, space, 1, comma, space, 1, right brace, end text

(Choice B, Checked, Correct)
CORRECT (SELECTED)
\text{\{51, 149, 140\}}{51, 149, 140}start text, left brace, 51, comma, space, 149, comma, space, 140, right brace, end text

(Choice C, Checked, Correct)
CORRECT (SELECTED)
\text{\{16, 63, 65\}}{16, 63, 65}start text, left brace, 16, comma, space, 63, comma, space, 65, right brace, end text

(Choice D, Incorrect)
INCORRECT
\text{\{6, 11, 8\}}{6, 11, 8}start text, left brace, 6, comma, space, 11, comma, space, 8, right brace, end text

Answer :

Option B : [tex]\{51,149,140\}[/tex] will form a right angled triangle.

Option C : [tex]\{16,63,65\}[/tex] will form a right angled triangle.

Explanation:

Option A : [tex]\{1,1,1}\}[/tex]

To determine whether the coordinates will form a right angled triangle, let us apply the Pythagorean theorem.

Thus, we have,

[tex]1^2+1^2=1^2[/tex]

  [tex]1+1=1[/tex]

        [tex]2\neq 1[/tex]

Since, both sides are not equal.

The set [tex]\{1,1,1}\}[/tex] will not form a right angled triangle.

Hence, Option A is not the correct answer.

Option B : [tex]\{51,149,140\}[/tex]

Let us apply Pythagorean theorem.

Thus, we have,

   [tex]51^2+140^2=149^2[/tex]

[tex]2601+19600=22201[/tex]

           [tex]22201=22201[/tex]

Since, both sides are equal.

The set [tex]\{51,149,140\}[/tex] will form a right angled triangle.

Hence, Option B is the correct answer.

Option C : [tex]\{16,63,65\}[/tex]

Let us apply Pythagorean theorem.

Thus, we have,

 [tex]16^2+63^2=65^2[/tex]

[tex]256+3969=4225[/tex]

         [tex]4225=4225[/tex]

Since, both sides are equal.

The set [tex]\{16,63,65\}[/tex] will form a right angled triangle.

Hence, Option C is the correct answer.

Option D : [tex]\{6,11,8\}[/tex]

Let us apply Pythagorean theorem.

Thus, we have,

[tex]6^2+8^2=11^2[/tex]

[tex]36+64=121[/tex]

     [tex]100\neq 121[/tex]

Since, both sides are not equal.

The set [tex]\{6,11,8\}[/tex] will not form a right angled triangle.

Hence, Option D is not the correct answer.

Other Questions