Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Since Points D, E trisect BC.
BD = DE = CE
Let BD = DE = CE = x
BE = 2x and BC = 3x
In the right ∆ABD,
AD2 = AB2 + BD2
AD2 = AB2 + x2 ...(1)
In the right ∆ABE,
AE2 = AB2 + 2BE2
AE2 = AB2 + 4x2 ...(2) ...(BE = 2x)
In the right ∆ABC
AC2 = AB2 + BC2
AC2 = AB2 + 9x2 ...(3) ...(BC = 3x)
R.H.S. = 3AC2 + 5AD2
= 3[AB2 + 9x2] + 5[AB2 + x2] ...[From (1) and (3)]
= 3AB2 + 27x2 + 5AB2 + 5x2
= 8AB2 + 32x2
= 8(AB2 + 4x2)
= 8AE2 ...[From (2)]
= R.H.S.
∴ 8AE2 = 3AC2 + 5AD2
APPEARS IN
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.
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.
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
30, 40, 50
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
9, 40, 41
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 a triangle having sides 8 cm, 15 cm and 17 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 ∆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?
