Advertisements
Advertisements
प्रश्न
Find the Pythagorean triplet from among the following set of numbers.
4, 5, 6
Advertisements
उत्तर
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.
संबंधित प्रश्न
From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove
that :
`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`
`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`
Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides.
Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)
Walls of two buildings on either side of a street are parallel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street, its top touches the window of the other building at a height 4.2 m. Find the width of the street.
In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.
In an isosceles triangle ABC; AB = AC and D is the point on BC produced.
Prove that: AD2 = AC2 + BD.CD.
In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm
In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.
