Advertisements
Advertisements
प्रश्न
If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.
Advertisements
उत्तर
The sides of the triangle are 6 cm, 8 cm and 10 cm.
The longest side is 10 cm.
(10)2 = 100 ….(i)
Now, the sum of the squares of the other two sides will be,
(6)2 + (8)2 = 36 + 64 = 100 ….(ii)
(10)2 = (6)2 + (8)2 ….. from (i) and (ii)
By the converse of Pythagoras theorem:
The given sides form a right angled triangle.
APPEARS IN
संबंधित प्रश्न
In a ∆ABC, AD ⊥ BC and AD2 = BC × CD. Prove ∆ABC is a right triangle
ABC is an equilateral triangle of side 2a. Find each of its altitudes.
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.
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?
For finding AB and BC with the help of information given in the figure, complete following activity.
AB = BC .......... 
∴ ∠BAC =
∴ AB = BC = × AC
= × `sqrt8`
= × `2sqrt2`
=
In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.
Prove that: 2AB2 = 2AC2 + BC2
In the given figure, AB//CD, AB = 7 cm, BD = 25 cm and CD = 17 cm;
find the length of side BC.
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
In Fig. 3, ∠ACB = 90° and CD ⊥ AB, prove that CD2 = BD x AD.
In the figure below, find the value of 'x'.
Find the Pythagorean triplet from among the following set of numbers.
4, 7, 8
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 60, 61
A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.
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
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 ______.
Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reasons for your answer.
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
