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
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
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
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
9, 40, 41
The area of a rectangle of length 21 cm and diagonal 29 cm is __________
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 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not.
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).
