Advertisements
Advertisements
Question
Find the Pythagorean triplet from among the following set of numbers.
4, 5, 6
Advertisements
Solution
It is known that, if in a triplet of natural numbers, the square of the biggest number is equal to the sum of the squares of the other two numbers, then the three numbers form a Pythagorean triplet.
The given set of numbers is (4, 5, 6).
The biggest number among the given set is 6.
62 = 36; 52 = 25; 42 = 16
Now, 25 + 16 = 41 ≠ 36
∴ 52 + 42 ≠ 62
Thus, (4, 5, 6) does not form a Pythagorean triplet.
RELATED QUESTIONS
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m;
find the distance between their tips.
A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.
In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.
A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?
If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.
