### Number Properties sample question - Squares - Right Triangles - Ascent Education - Mock TANCET Tests

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# Number Properties : Squares - Right Triangles

The question is from the topic number systems / trigonometry.

## Question

'a' and 'b' are the lengths of the base and height of a right angled triangle whose hypotenuse is 'h'. If the values of 'a' and 'b' are positive integers, which of the following cannot be a value of the square of the hypotenuse?
1. 13
2. 23
3. 37
4. 41
Correct Answer - 23. Choice (2)

Pythagoras Theorem : The square of the hypotenuse = h2 = a2 + b2

As the problem states that 'a' and 'b' are positive integers, the values of a2 and b2 will have to be perfect squares. Hence we need to find out that value amongst the four answer choices which cannot be expressed as the sum of two perfect squares.

Choice 1 is 13. 13 = 9 + 4 = 32 + 22. Therefore, Choice 1 is not the answer as it is a possible value of h2

Choice 2 is 23. 23 cannot be expressed as the sum two numbers, each of which in turn happen to be perfect squares. Therefore, Choice 2 is the answer.

Choice 3 is 37. 37 = 36 + 1 = 62 + 12. Therefore, Choice 3 is not the answer as it is a possible value of h2

Choice 4 is 41. 41 = 25 + 16 = 52 + 42. Therefore, Choice 4 is not the answer as it is a possible value of h2

Level of difficulty : Moderate

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