Answer:
see explanation
Step-by-step explanation:
Using Pythagoras' identity on the right triangles, that is
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the missing side, then
13² = 5² + x²
169 = 25 + x² ( subtract 25 from both sides )
144 = x² ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12
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let h be the hypotenuse, then
h² = 24² + 45² = 576 + 2025 = 2601 ( take the square root of both sides )
h = [tex]\sqrt{2601}[/tex] = 51
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Using the converse of Pythagoras' identity, that is
If the square of the longest side equals the sum of the squares on the other 2 sides then the triangle is right.
3, 4, 5
5² = 25 and 3² + 4² = 25 ⇒ right triangle
6, 8, 10
10² = 100 and 6² + 8² = 100 ⇒ right triangle
16, 63, 65
65² = 4225 and 16² + 63² = 4225 ⇒ right triangle
8, 9, 10
10² = 100 and 8² + 9² = 145 ⇒ not a right triangle
