Home » Aptitude » Volume and Surface Area

Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?

Q: Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?

let n-1, n, n+1 be 3 consecutive integers So (n+1)^2= n^2+ (n-1)^2 (n+1)^2-(n-1)^2= n^2 4n = n^2 So n = 0 or n = 4 n can’t be 0 as n-1 will be negative then So 3,4 and 5 is the only triplet formed.

Only one
Only two
Only three
Infinitely many

Correct Answer: Only one

Explanation:

let n-1, n, n+1 be 3 consecutive integers

(n+1)^2= n^2+ (n-1)^2

(n+1)^2-(n-1)^2= n^2

4n = n^2

So n = 0 or n = 4

n can’t be 0 as n-1 will be negative then

So 3,4 and 5 is the only triplet formed.

← Previous Question Next Question→

More Questions from Volume and Surface Area

Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 square cm
A rectangular red carpet of size 6 ft ×12 ft has a dark red border 6 inches wide. What is the area of the dark red border?
Consider the following statements: 1) An isosceles trapezium is always cyclic. 2) Any cyclic parallelogram is a rectangle. Which of the above statements is/are correct?
Consider the following statements: 1) The number of circles that can be drawn through three non-collinear points is infinity. 2) Angle formed in minor segment of a circle is acute. Which of the above statements is/are correct?
Consider the following statements: 1) The number of circles that can be drawn through three non-collinear points is infinity. 2) Angle formed in minor segment of a circle is acute. Which of the above statements is/are correct?
Consider the following inequalities in respect of any triangle ABC: 1) AC –AB < BC 2) BC –AC < AB 3) AB –BC < AC Which of the above are correct?
ABC is a right angled triangle in which ∠A = 90°, AB = 5 cm and AC = 12 cm. What is the approximate volume (in cm3) of the double cone formed by rotating the triangle about its hypotenuse?
PQ is a diameter of a circle with centre O. RS is a chord parallel to PQ subtends an angle of 40° at the centre of the circle. If PR and QS are produced to meet at T, then what will be the measure (in degrees) of ∠PTQ?
The diagonal of a square is 10 cm. What is the length (in cm) of its side?
Point A divides segment BC in the ratio 5:1. Co-ordinates of B are (6 ,-4) and C are (0,8). What are the co-ordinates of point A?

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion