Advertisements
Advertisements
प्रश्न
A rectangle having dimensions 35 m × 12 m, then what is the length of its diagonal?
Advertisements
उत्तर

Let □PQRS be the given rectangle.
In ∆PQR,
∠Q = 90° ....[Angle of a rectangle]
∴ PR2 = PQ2 + QR2 .....[Pythagoras theorem]
= 122 + 352
= 144 + 1225
= 1369
∴ PR = `sqrt(1369)` ......[Taking square root of both sides]
= 37 cm
∴ The length of the diagonal of the given rectangle is 37 cm.
संबंधित प्रश्न
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?

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
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
If the sides of a triangle are in the ratio 5 : 12 : 13 then, it is ________
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
8, 15, 17
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
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
24, 45, 51
Choose the correct alternative:
If the length of diagonal of square is √2, then what is the length of each side?
Choose the correct alternative:
If length of both diagonals of rhombus are 60 and 80, then what is the length of side?
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).

