Advertisements
Advertisements
प्रश्न
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
Advertisements
उत्तर
In the triplet (5, 12, 13),
52 = 25,
122 = 144,
132 = 169
52 + 122 = 25 + 144 = 169
The square of the largest number is equal to the sum of the squares of the other two numbers.
∴ (5, 12, 13) is a pythagorean triplet.
APPEARS IN
संबंधित प्रश्न
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right traingle ,right-angled at B. Find the values of p.
In figure, ∠B of ∆ABC is an acute angle and AD ⊥ BC, prove that AC2 = AB2 + BC2 – 2BC × BD
ABC is a right triangle right-angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB, prove that
(i) cp = ab
`(ii) 1/p^2=1/a^2+1/b^2`
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals
ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.

In ΔMNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Choose the correct alternative:
In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P?
Find the side of the square whose diagonal is `16sqrt(2)` cm.
In the figure below, find the value of 'x'.

Find the Pythagorean triplet from among the following set of numbers.
2, 4, 5
Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.
From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = AE2 + CD2 + BF2
A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that OB2 + OD2 = OC2 + OA2
A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
In a quadrilateral ABCD, ∠A + ∠D = 90°. Prove that AC2 + BD2 = AD2 + BC2
[Hint: Produce AB and DC to meet at E.]
In a right-angled triangle ABC, if angle B = 90°, then which of the following is true?
The longest side of a right angled triangle is called its ______.
Two squares having same perimeter are congruent.
Points A and B are on the opposite edges of a pond as shown in the following figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.

