Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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?
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
24, 45, 51
The area of a rectangle of length 21 cm and diagonal 29 cm is __________
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.
