Advertisements
Advertisements
Question
Find the Pythagorean triplet from among the following set of numbers.
3, 4, 5
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 (3, 4, 5).
The biggest number among the given set is 5.
52 = 25; 42 = 16; 32 = 9
Now, 16 + 9 = 25
∴ 42 + 32 = 52
Thus, (3, 4, 5) form a Pythagorean triplet.
RELATED QUESTIONS
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)
For finding AB and BC with the help of information given in the figure, complete following activity.
AB = BC .......... 
∴ ∠BAC =
∴ AB = BC = × AC
= × `sqrt8`
= × `2sqrt2`
=
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
In ΔABC, Find the sides of the triangle, if:
- AB = ( x - 3 ) cm, BC = ( x + 4 ) cm and AC = ( x + 6 ) cm
- AB = x cm, BC = ( 4x + 4 ) cm and AC = ( 4x + 5) cm
In figure AB = BC and AD is perpendicular to CD.
Prove that: AC2 = 2BC. DC.
If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.
In a right-angled triangle ABC, if angle B = 90°, BC = 3 cm and AC = 5 cm, then the length of side AB is ______.
Two squares are congruent, if they have same ______.
