Solve this: Q 8 The lengths of the sides of the triangle are given in centimetres as: - Maths - Simultaneous Linear Equations

Question

Solve this:

Q 8 The lengths of the sides of the triangle are given in
centimetres as:

2 x   +   y 2 ,   2 x 3 + 2 y + 5 2   a n d
  y + 5 x 3 + 1 2

If the triangle is equilateral, prove that the triangle whose sides
are (2xy+1), (2x+1) and (6y+1) cm each is also
equilateral

Devansh Shah · Accepted Answer

Dear Student,

In the given question, it is given that that the triangle is
equilateral

The three sides are given as:

S1 = 2x + y2 , S2 =  2x3 + 2y + 52 , S3 =  y + 5x3 + 12So ,for S1 and S2, S1 = S2 2x + y2 = 2x3 + 2y + 524x + y2 = 4x+12y+15612x + 3y = 4x + 12y + 158x - 9y = 15     ------1For S2 and S3, S2 = S32x3 + 2y + 52 = y + 5x3 + 124x+12y+156 = 6y + 10x + 366x - 6y = 12x-y = 2x=2+ySubstituting value of x in 1, 8x - 9y = 158(2+y) -9y = 1516 + 8y -9y = 15y = 1x = 2+y=2+1 = 3

Now, the three sides for triangle 2 are given as:

T1 = 2xy + 1 = 2×3×1 + 1 = 7T2 = 2x+1 = 2×3 + 1 = 7T3 = 6y+1 = 6×1 + 1 = 7Since T1=T2=T3, Triangle 2 is also equilateral

Hope it helps

Regards

Solve this: Q. 8 The lengths of the sides of the triangle are given in centimetres as: 2 x + y 2 , 2 x 3 + 2 y + 5 2 a n d y + 5 x 3 + 1 2 . If the triangle is equilateral, prove that the triangle whose sides are (2xy+1), (2x+1) and (6y+1) cm each is also equilateral.