Advertisements
Advertisements
प्रश्न
Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)
Advertisements
उत्तर
In the triplet (11, 60, 61),
112 = 121, 602 = 3600, 612 = 3721 and 121 + 3600 = 3721
The square of the largest number is equal to the sum of the squares of the other two numbers.
∴ (11, 60, 61) is a pythagorean triplet.
APPEARS IN
संबंधित प्रश्न
Side of a triangle is given, determine it is a right triangle.
`(2a – 1) cm, 2\sqrt { 2a } cm, and (2a + 1) cm`
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
Tick the correct answer and justify: In ΔABC, AB = `6sqrt3` cm, AC = 12 cm and BC = 6 cm.
The angle B is:
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.
In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°.
Prove that: 2AC2 - AB2 = BC2 + CD2 + DA2
Prove that `(sin θ + cosec θ)^2 + (cos θ + sec θ)^2 = 7 + tan^2 θ + cot^2 θ`.
Prove that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :
(i) AC
(ii) CD

In the figure below, find the value of 'x'.

Find the Pythagorean triplet from among the following set of numbers.
9, 40, 41
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.
In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
In a right angled triangle, the hypotenuse is the greatest side
Sides AB and BE of a right triangle, right-angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is ______.

If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.
The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.
