Question

1. Which set of numbers
could represent the legth of
the 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}

Answer 1

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:

$(Hypotenuse)^{2} = Base^{2} + Altitude^{2}$

where largest side is the hypotenuse.

Case 1:  $(10)^{2} \neq (5)^{2} + (5)^{2}$

∵ 100 ≠ 50

Case 2:  $(6)^{2} \neq (4)^{2} + (5)^{2}$

36 ≠ 16 + 25

36 ≠ 41

Case 3: $(13)^{2} = (5)^{2} + (12)^{2}$

169 = 25 + 144

169 = 169

Since $(Hypotenuse)^{2} = Base^{2} + Altitude^{2} = 169$, ∴ 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:  $(10)^{2} \neq (7)^{2} + (8)^{2}$

100 ≠ 49 + 64

100 ≠ 103