मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Identify, with Reason, If the Following is a Pythagorean Triplet.

Advertisements
Advertisements

प्रश्न

Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)

बेरीज
Advertisements

उत्तर

In the triplet (4, 9, 12),
42 = 16, 92 = 81, 122 = 144 and 16 + 81 = 97 ≠ 144
The square of the largest number is not equal to the sum of the squares of the other two numbers.
∴ (4, 9, 12) is not a pythagorean triplet.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Pythagoras Theorem - Practice Set 2.1 [पृष्ठ ३८]

APPEARS IN

बालभारती Geometry Mathematics 2 [English] Standard 10 Maharashtra State Board
पाठ 2 Pythagoras Theorem
Practice Set 2.1 | Q 1.2 | पृष्ठ ३८

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 13 cm, 12 cm, 5 cm


ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2 


ABC is an equilateral triangle of side 2a. Find each of its altitudes.


In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:

`"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`


Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?


In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.


A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.


In ΔABC,  Find the sides of the triangle, if:

  1. AB =  ( x - 3 ) cm, BC = ( x + 4 ) cm and AC = ( x + 6 ) cm
  2. AB = x cm, BC = ( 4x + 4 ) cm and AC = ( 4x + 5) cm

In a rectangle ABCD,
prove that: AC2 + BD2 = AB2 + BC2 + CD2 + DA2.


M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2


If P and Q are the points on side CA and CB respectively of ΔABC, right angled at C, prove that (AQ2 + BP2 ) = (AB2 + PQ2)


Use the information given in the figure to find the length AD.


In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 = AD2 - BC x CE + `(1)/(4)"BC"^2`


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2AD2 + `(1)/(2)"BC"^2`


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


The perpendicular PS on the base QR of a ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ2 = 2PR2 + QR2 


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.]


Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×