Advertisements
Advertisements
प्रश्न
In ΔABC, AB = 9 cm, BC = 40 cm, AC = 41 cm. State whether ΔABC is a right-angled triangle or not. Write reason.
Advertisements
उत्तर
Sides of ΔABC are AB = 9 cm, BC = 40 cm, AC = 41 cm
The triangle's longest side measures 41 cm.
∴ (41)2 = 1681 ......(i)
Now, the total of the remaining sides squared is
(9)2 + (40)2 = 81 + 1600
= 1681 ......(ii)
From equations (i) and (ii), the given sides form a right-angle triangle.
Because the square of the longest side equals the sum of the squares of the remaining two sides. .....[Converse of Pythagoras theorem]
APPEARS IN
संबंधित प्रश्न
In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?
In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?
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 the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE2 = 3AC2 + 5AD2
If in ∆ABC, DE || BC. AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
If the sides of a triangle are in the ratio 5 : 12 : 13 then, it is ________
8, 15, 17 is a Pythagorean triplet
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
12, 13, 15
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
9, 40, 41
The area of a rectangle of length 21 cm and diagonal 29 cm is __________
In right angled triangle, if sum of the squares of the sides of right angle is 169, then what is the length of the hypotenuse?
A rectangle having length of a side is 12 and length of diagonal is 20, then what is length of other side?
If the length of diagonal of square is `sqrt(2)`, then what is the length of each side?
If length of both diagonals of rhombus are 60 and 80, then what is the length of side?
If a triangle having sides 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not
If a triangle having sides 8 cm, 15 cm and 17 cm, then state whether given triangle is right angled triangle or not
In ∆LMN, l = 5, m = 13, n = 12 then complete the activity to show that whether the given triangle is right angled triangle or not.
*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)
Activity: In ∆LMN, l = 5, m = 13, n = `square`
∴ l2 = `square`, m2 = 169, n2 = 144.
∴ l2 + n2 = 25 + 144 = `square`
∴ `square` + l2 = m2
∴ By Converse of Pythagoras theorem, ∆LMN is right angled triangle.
In a right angled triangle, right-angled at B, lengths of sides AB and AC are 5 cm and 13 cm, respectively. What will be the length of side BC?
