Question

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

Answer 1

10, 24, 26

this set is the one that satisfies the sides of a right-angled trinagle as it follows the Pythg Theorem

10^2 + 24^2 = 676 =  26^2

Answer 2

Answer:

(B) 10, 24, 26

Step-by-step explanation:

We have to find which set of the numbers can represent the side lengths of a right triangle.

Since, we are given a right triangle, thus we can use the Pythagoras theorem to determine the side lengths, thus

(A) 8, 12 and 15

Applying the Pythagoras theorem ,we have

$(15)^{2}=(12)^{2}+(8)^{2}$

$225=144+64$

$225=208$

which is not possible, thus this option is incorrect.

(B)10, 24, 26

Applying the Pythagoras theorem ,we have

$(26)^{2}=(24)^{2}+(10)^{2}$

$676=576+10$

$676=676$

which is possible, thus this is the correct option.

(C)12, 20, 25

Applying the Pythagoras theorem ,we have

$(25)^{2}=(20)^{2}+(12)^{2}$

$625=400+144$

$625=544$

which is not possible, thus this option is incorrect.

(D) 15, 18, 20

Applying the Pythagoras theorem ,we have

$(20)^{2}=(18)^{2}+(15)^{2}$

$400=324+225$

$400=549$

which is not possible, thus this option is incorrect.

Therefore, the side lengths of the given right triangle are:

10cm, 24cm and 26 cm.