Question

select all the sets that are the three side lengths of right triangles A.8,7,15 B.4, 10, √84 C. √8, 11, √129 D. √1, 2, √3

Answer 1

Answer:

B.4, 10, √84

C. √8, 11, √129

D. √1, 2, √3

Step-by-step explanation:

For any set of three side length of a triangle to be a right angled triangle, the sum of the square of the two of the sides must be equal to the square of the longest side according to pythagoras theorem.

The longest side is always the hypotenuse

For option D, 2 will be the longest side. Since 2 is the hypotenuse, the sum of the square of other two values must be equivalent to the square of 2,

$= (\sqrt{1})^{2} + (\sqrt{3})^{2} \\ = 1=3\\= 4\\= 2^{2} (hypotenuse)$

This shows that √1, 2, √3 are three sides of a right triangles.

Similarly for option C, the hypotenuse is √129 being the largest.

To show the sides are that of a right triangles;

$= (\sqrt{8}) ^{2} + 11^{2} \\= 8 + 121\\= 129\\= (\sqrt{129})^{2}$

Since the resulting  value is the square of the hyp, then √8, 11, √129 are three sides of a right triangles.

For option B; 10 is the hypotenuse being the longest sides, To show the sides are that of a right triangles;

$=4^{2}+(\sqrt{84})^{2} \\ = 16+84\\= 100\\= 10^{2}$

Since the resulting  value is the square of the hyp, then 4, 10, √84  are three sides of a right triangles.

Only option A is wrong since 15² is not equal to the sum of 8² and 7².