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 the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?
The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle
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
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
The incentre is equidistant from all the vertices of a triangle
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
30, 40, 50
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 __________
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?
In ∆ABC, AB = `6sqrt(3)` cm, AC = 12 cm, and BC = 6 cm then m∠A = ?
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 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?
