00:01
So in this question it is given that quadratal a, b, c, b, c, is the icct is the icct and we have to find x, y, b, f, ef, k, e, d, b, f, and b c, given ef is the median of this iocel's trapeword, abct, and all the sides are given, that is bf equal to 5a minus 6, ef equal to 2f plus 10, d .c equal to 8x minus 15, and ed equal to 2a plus 3, okay.
00:29
Now, since this ef is a median of this isosal triangle, okay, so we can say that ae is equal to ed, similarly bf is equal to, similarly bf is equal to f c, okay.
00:43
So now if ae equal to ed, then ae will be equal to ed equal to 2a plus 3, similarly bf will be equal to fc equal to 5 by minus 6, okay.
00:55
Now in this isosal trapezoid, ad will be called b c, b c, c.
01:00
Okay because the opposite sides are equal, non -parallel sides are equal.
01:04
Hence we can say that what is ad? ad is nothing but ae plus ed, okay and aed are equal so you can say that ad is nothing but 2 into 2a plus 3.
01:16
Similarly what is b .c is nothing but 2 into f5 minus 6.
01:20
So we will equate both the ad and bc because they are equal.
01:26
So we get when we get we get 2 into 2.
01:31
2 x2 x2 x2 will get cancelled out and we'll remain it 2a plus 3 equal to 5 by minus 6 so solving we get y equal to 3 okay so we get y equal to 3 now we'll solve for x so how can we establish a relation of x we know that this is a property by property of isosos stratagoid the median that is ef is equal to half of the summation of the parallel sides okay so ef will be equal to half of ab plus cd so ef equal to half of ab so what is e.
02:02
Ef is 2x plus 10, ab is 8x minus 15, cd is 10.
02:06
So solving for x, we get 2 into 2x plus 10 equal to 8x minus 10, that is 8x minus 5.
02:11
So 4x plus 20 is equal to 8x minus 5...