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

(5, 12, 13) are the set of numbers that could represent the length of a right triangle.

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) \\eq (5)^(2) + (5)^(2)`

∵ 100 ≠ 50

Case 2:
`(6)^(2) \\eq (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) \\eq (7)^(2) + (8)^(2)`

100 ≠ 49 + 64

100 ≠ 103