1. Which set of numberscould represent the legth ofthe sides of a right triangle?(1) {5, 5, 10} abutis(2) {4, 5, 6} Tolosia alga(3) {5, 12, 13} cluoibog(4) {7, 8, 10}
Accepted Solution
A:
Answer:(5, 12, 13) are the set of numbers that could represent the length of a right triangle.Step-by-step explanation:In any right angle triangle sum of square of the largest side is equal to the sum of square of the other two sides.Using pythagoras:[tex](Hypotenuse)^{2} = Base^{2} + Altitude^{2}[/tex]where largest side is the hypotenuse.Case 1: [tex](10)^{2} \neq (5)^{2} + (5)^{2}[/tex]∵ 100 ≠ 50Case 2: [tex](6)^{2} \neq (4)^{2} + (5)^{2}[/tex]36 ≠ 16 + 2536 ≠ 41Case 3: [tex](13)^{2} = (5)^{2} + (12)^{2}[/tex]169 = 25 + 144169 = 169Since [tex](Hypotenuse)^{2} = Base^{2} + Altitude^{2} = 169[/tex], ∴ option C is the correct answer. So, (5, 12, 13) are the set of numbers that could represent the length of a right triangle.Case 4: [tex](10)^{2} \neq (7)^{2} + (8)^{2}[/tex]100 ≠ 49 + 64100 ≠ 103