Advertisements
Advertisements
Question
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.
Advertisements
Solution
In ∆LMN, l = 5, m = 13, n = \[\boxed{12}\]
∴ l2 = \[\boxed{25}\], m2 = 169, n2 = 144.
∴ l2 + n2 = 25 + 144 = \[\boxed{169}\]
∴ \[\boxed{n^2}\] + l2 = m2
∴ By Converse of Pythagoras theorem, ∆LMN is right angled triangle.
RELATED QUESTIONS
In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?
Sides of the triangle are 7 cm, 24 cm, and 25 cm. Determine whether the triangle is a right-angled triangle or not.
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
In a ∆ABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC 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
24, 45, 51
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?
If the length of diagonal of square is `sqrt(2)`, then what is the length of each side?
In ∆ABC, AB = `6sqrt(3)` cm, AC = 12 cm, and BC = 6 cm then m∠A = ?
If a triangle having sides 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not
A rectangle having dimensions 35 m × 12 m, then what is the length of its diagonal?
In ΔABC, AB = 9 cm, BC = 40 cm, AC = 41 cm. State whether ΔABC is a right-angled triangle or not. Write reason.
In the given figure, triangle PQR is right-angled at Q. S is the mid-point of side QR. Prove that QR2 = 4(PS2 – PQ2).
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?
