Question

1 Which of the following could be the sides of a right triangle? Check all that apply. A. 10, 24, 26 B. 4, 5, 9 C. 18, 24, 30​

Answer 1

Answer:

A and C

Step-by-step explanation:

Let Triangle ABC is a right angle traingle.

From Option A

AB= 24, BC= 26 and AC=10

By Pythagorean Triplet

(AB)^2 + (AC)^2 = (24)^2 + (10)^2

= 576+100

(AB)^2 + (AC)^2 = 676 ---------------- (I)

(BC)^2 = 26^2 = 676 -------------------(ii)

From (I) and (ii)

(BC)^2 = (AB)^2 + (AC)^2

Therefore, the sides 10,24 and 26 are the sides of the right angle triangle.

From Option C

AB= 18, BC= 30 and AC=24

By Pythagorean Triplet

(AB)^2 + (AC)^2 = (18)^2 + (24)^2

= 324+576

(AB)^2 + (AC)^2 = 900---------------- (I)

(BC)^2 = 30^2 = 900 -------------------(ii)

From (I) and (ii)

(BC)^2 = (AB)^2 + (AC)^2

Therefore, the sides 18, 24 and 30 are the sides of the right angle triangle.