English
Maharashtra State BoardSSC (English Medium) 10th Standard

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

Advertisements
Advertisements

Question

Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)

Sum
Advertisements

Solution

 In the triplet (3, 5, 4),
32 = 9, 52 = 25, 42 = 16 and 9 + 16 = 25
The square of the largest number is equal to the sum of the squares of the other two numbers.
∴ (3, 5, 4) is a pythagorean triplet.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Pythagoras Theorem - Practice Set 2.1 [Page 38]

APPEARS IN

Balbharati Geometry Mathematics 2 [English] Standard 10 Maharashtra State Board
Chapter 2 Pythagoras Theorem
Practice Set 2.1 | Q 1.1 | Page 38

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

ABCD is a rhombus. Prove that AB2 + BC2 + CD2 + DA2= AC2 + BD2


In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2 : 1. Prove that

`(i) 9 AQ^2 = 9 AC^2 + 4 BC^2`

`(ii) 9 BP^2 = 9 BC^2 + 4 AC^2`

`(iii) 9 (AQ^2 + BP^2 ) = 13 AB^2`


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 with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.


D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE+ BD2 = AB2 + DE2


 
 

In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD2 = 7 AB2

 
 

Which of the following can be the sides of a right triangle?

2.5 cm, 6.5 cm, 6 cm

In the case of right-angled triangles, identify the right angles.


Find the length diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.


In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL+ CM2) = 5 BC2


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 triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.


Find the Pythagorean triplet from among the following set of numbers.

2, 6, 7


Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.


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


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED


In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP2 = 9BC2 + 4AC2


In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2 


From given figure, In ∆ABC, If AC = 12 cm. then AB = ?


Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°

∠BAC = `square`

∴ ∆ABC is 30° – 60° – 90° triangle.

∴ In ∆ABC by property of 30° – 60° – 90° triangle.

∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC

∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`

∴ `square` = 6 and BC = `6sqrt(3)`


A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.


Jiya walks 6 km due east and then 8 km due north. How far is she from her starting place?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×