MATH SOLVE

5 months ago

Q:
# Which set of numbers can represent the side lengths, in centimeters, of a right triangle?0 8, 12, 15O 10, 24, 26O 12, 20, 2515, 18, 20Mark this and retumSave and ExitNext

Accepted Solution

A:

Answer:The set {10 , 24 , 26} formed a right triangleStep-by-step explanation:* Lets explain how to check the sides lengths which formed a right triangle- In triangle ABC# If AC is the longest side in length# If (AC)² = (AB)² + (BC)²∴ AB , BC , AC formed a right angle triangle ∴ m∠B = 90° (The angle opposite to the longest side)∴ AC is the hypotenuse* Now lets solve the problem- In set 8 , 12 , 15∵ The longest side is 15 cm∴ (15)² = 225∵ (8)² + (12)² = 64 + 144 = 208∵ (15)² ≠ (8)² + (12)²∴ The set not formed a right triangle- In set 10 , 24 , 26∵ The longest side is 26 cm∴ (26)² = 676∵ (10)² + (24)² = 100 + 576 = 676∵ (26)² = (10)² + (24)²∴ The set formed a right triangle- In set 12 , 20 , 25∵ The longest side is 25 cm∴ (25)² = 625∵ (12)² + (20)² = 144 + 400 = 544∵ (25)² ≠ (12)² + (20)²∴ The set not formed a right triangle- In set 15 , 18 , 20∵ The longest side is 20 cm∴ (20)² = 400∵ (15)² + (18)² = 225 + 324 = 549∵ (20)² ≠ (15)² + (18)²∴ The set not formed a right triangle* The set {10 , 24 , 26} formed a right triangle